Sharp EL-W506T vs. Sharp EL-W516T

[Guy Macon]

What is the difference between the Sharp EL-W506T and the Sharp EL-W516T?
I am trying to figure out what the top of the line Sharp non-programmable non-graphing scientific calculator is so I can compare it with the Hewlett Packard HP-35S, Casio fx-991EX and Texas Instruments TI-36X Pro.

[rprosperi]

(11-10-2019 11:14 AM)Guy Macon Wrote:  What is the difference between the Sharp EL-W506T and the Sharp EL-W516T?
I am trying to figure out what the top of the line Sharp non-programmable non-graphing scientific calculator is so I can compare it with the Hewlett Packard HP-35S, Casio fx-991EX and Texas Instruments TI-36X Pro.

It appears the EL-506T is newer, though I can't say what the difference is between them.

The Sharp website lists the EL-W506T and not the 516, and is current as of September '19

[lrdheat]

Complicating the comparison is the different versions offered in different countries. The TI 30X Pro MathPrint, offered in Europe, is a faster version of the 36X Pro offered in the U.S. The European version accepts equations with a larger number of characters than the 36X Pro as well, offers stats for 50 lines of data. The CASIO 991 EX has various versions that offer slightly different function sets as well. The biggest difference to me between the CASIO’s and TI’s is CASIO loses history when turned off, and TI allows functions to be placed in f1 and f2, allowing for use elsewhere in the calculator such as in integration or other analysis. The 991EX requires the function to be rewritten for each use elsewhere in the calculator. The 991 EX can accept longer lists for statistical work, but loses this data upon turning unit off.

[Guy Macon]

(11-10-2019 02:15 PM)rprosperi Wrote:  It appears the EL-506T is newer, though I can't say what the difference is between them.

The Sharp website lists the EL-W506T and not the 516, and is current as of September '19

Hmmm. I just tried shopping for one, and all the vendors (not just Amazon, but a bunch of different sites found with Google shopping) either show this:

https://www.amazon.com/dp/B078WRWS6Q/

https://images-na.ssl-images-amazon.com/...L._AC_.jpg

or this:

https://www.amazon.com/dp/B06XKLKNX9/

https://images-na.ssl-images-amazon.com/...L1500_.jpg

...which, of course, contradicts the Sharp website:

http://www.sharp-calculators.com/en/cont...6-el-w506t

I am holding in my hand a calculator that says "Sharp EL-W516T" on the front and Sharp EL-W516TB-SL (The BSL means "black slimline") on the blister pack. I checked very carefully and it is 100% identical with the EL-W506T Sharp shows on the website except for the model number, and advertises the same 640 functions.

Arrrgh! Why do calculator manufacturers DO this??

[Eddie W. Shore]

Good question. I sometimes have a hard time keeping the Casio scientific calculators apart.

I think the 516 and 506 are similar and both have calculus functions.

[rprosperi]

All the Sharp EL-Wnnn... utilize the "WriteView" feature, which is marketing speak for displaying algebraic equations in 'graphical' form (meaning fraction, integral and root symbols, etc. not true graphics). Models that don't have the 'W' prefix in the model don't have that capability. Most often (but not 100% of the time) the trailing letters are for colors, cover stle, and other pkg. type tweaks.

[ijabbott]

I guess there are just minor regional differences between the EL-W516T (chiefly North America) and EL-W506T (chiefly Europe and rest of the world). Similar to the situation with Casio fx-115ES Plus versus fx-991ES Plus.

[Mjim]

My first post here, but it seems hard to find a good active forum for chatting about calculators and this seems to be pretty active. I mostly mess around with Casio & Sharp as they seem to be plenty good enough for my purpose at the moment, but I do have an HP49G+ (which I am horrid at using, I did a few tutorials on RPN and I do like it, but I can't seem to help accidentally clearing the stack all the time), although as I gain a bit more mathematical knowledge I'll have to revisit using that again.

Hopefully doesn't get flagged as spam, but I think it's likely the EL-W506T & EL-W516T are identical much like the EL-W506X & EL-W516X that came before. There is room for doubt, but the product guide (Page 32) on Sharp's website list the EL-W506T as having 640 functions which from what I can see is the same as the Sharp EL-W516T.

Here is a link to that product guide as well as some other useful stuff, though it is easy enough to google:
http://www.sharp-calculators.com/en/cont...-downloads

I'll recommend grabbing the Operational guide for the EL-W506T as this has a bit more detail then the bundled instruction manual. There are still some holes though; for example I hear complaints with the Sharp's constant 'k' ability which is only mentioned in passing. Check out https://global.sharp/contents/calculator...index.html for a better idea of what causes 'k' to appear.

Even has an emulator for the EL-W506T (no apparent time limit like the Casio emulators).

It's worth noting that the EL-W506T loses the 4 formula storage memories. Personally I think that is a rather understated downgrade, as the amount of lines stored in multi-line playback is dependent on the size of the formulas and numbers entered. For example this equation will only allow about 2 lines of multi-line playback (everything to the right of the integral, the left is just the Sharp equivalent to the right (The Sharp EL-W506X/T uses the Simpson algorithm for estimating definite integrals):



b = upper limit, a = lower limit, d = number of double divisions to use for the interval (Simpson's needs to have divisions that are multiples of 2, so if d=64, we actually break up the graph into 128 chunks to calculate the area).

When dealing with big formula's the last thing you want to be doing is retyping in them, so if you want to use that formula again, you need to keep scrolling up to run the equation to make sure it stays in memory. Being able to store 4 big equations like these completely removes any apprehension of accidentally pushing your formula off the multi-line 'stack'.

Looking at the manual, the buffer is about 159 characters, so since this equation is pretty close to that limit, 2 entries matches up with the 340 characters or so quoted for multi-line playback for the EL-W506X/516X. With 4 function memories that extends the effective memory close to a thousand.

That being said, the implementation of the table function on the EL-W506T is very well done, it just calculates as it goes, so there is no limit to what you can view, set the starting interval, interval size and away you go. I recommend giving the emulator a whirl to see how it works.

[Pjwum]

My daughter had to buy an EL-W506X for her math course at school. This is essentially a W506T without WriteView. When she allowed me to play with it I tried one of my standard tests, the definite integral int(0, 6, exp(x^3),x). The result came up quite fast but was way off (the fx-991DE is dead on btw.).
I was curious about the algorithm they implemented and found, they use Simpson's formula but would never calculate more than n=100 intervals. No matter the precision needed or fixed digits.
This makes it rather unreliable when used for integrals.
Patrick

[rprosperi]

(11-13-2019 06:27 PM)Pjwum Wrote:  This makes it rather unreliable when used for integrals.

Though probably just perfect for any integral your daughter will encounter... and likely anyone else that doesn't seek pathological equations to integrate. .

Don't get me wrong, I do it too, but never mistake that sort of recreation with real-world problems, especially in High School.

Also, the EL-W506X does indeed have WriteView, it says it right on the face of the calculator above the LCD. As noted above, the "W" in all the EL-Wxxx models means that they do have WriteView. Maybe you meant the EL-506X, which indeed does not have WriteView.

[Mjim]

The Sharp EL-W516x (and presumably the newer EL-W506T) seems to handle a pretty big number of divisions though; I tried a division count of 131,072 which worked fine, although you are probably going to want to go up the road and purchase some biscuits and boil the jug while you wait.

I'm guessing you meant the EL-506X, in which case I agree that being limited to n=100 seems pretty small unless you are dealing with small changes in area. The Casio fx-570MS, which also uses the Simpson method, can handle up to 2^n where you can choose a maximum value of n=9, or 512 divisions which is significantly better.

I'm off now on a Tangent about the Casio MS series, so please skip if uninterested!:
What though impresses me especially about the Casio MS series integration (despite not being as flash as the ES & EX series with it's faster and more accurate integration algorithm) is that it truncates the integration result to a certain number of significant figures depending on the number of the divisions and the function.

It really seems to be truncating the uncertain digits based on an internal error range calculation, but I find it hard to believe it uses the Simpson's rule error function since it requires calculating the 4th derivative of the function first and finding it's maximum....I mean if it was really calculating the error function, that is more impressive then taking the integral as far as I'm concerned

Simpson Error function is |Es| at the bottom of this linked page: http://tutorial.math.lamar.edu/Classes/C...grals.aspx

You can see this error function at work, take the function e^x (done on Casio fx-82MS temporarily upgraded to fx-570MS):

Interval [0,1]:
integrate(e^x,0,1,n=4) = 1.71828
integrate(e^x,0,1,n=6) = 1.71828183

Interval [0,2]
integrate(e^x,0,2,n=4) = 6.389
integrate(e^x,0,2,n=6) = 6.389056

With the Simpson error function it is always taking the absolute maximum of the 4th derivative, so by extending the interval to 2, we get a steeper interval and so higher maximum error (ie e^x when x=2, and since the derivative of e^x is just e^x, so will it's forth derivative be). This seems to be what is happening in the above examples, which explains why you have less digits over the larger interval despite using the same number of divisions. Regardless of how they did it, it amazes me that they managed to pull it off on a calculator that doesn't even have natural textbook entry.

In addition, if the confidence is too low it will throw a math error:
integrate(e^x,0,0.1,n=1) = 0.1052 (Casio auto-algorithm logic selects n=3)
integrate(e^x,0,1,n=1) = 2 (Casio auto-algorithm logic selects n=3)
integrate(e^x,0,2,n=1) = Math Error (Casio auto-algorithm logic selects n=5)

I can't say for certain what error checking algorithm is being used, but as long as the estimate gives an equivalent or higher error range back it means you can count on the digits you see. From a bit of testing:

integrate(e^(x^2),0,5):
Wolfram answer: 7,354,153,747.83713

64 Divisions:
Casio: 7,000,000,000
Sharp: 7,368,738,187
|Es| <= 26,106,748.11

Adding the error in the actual result is somewhere between:
7,342,631,439 - 7,394,844,935

The first 2 significant figures could be either 73 or 74 so the Casio gave the correct result back as you can rely only on the first significant figure.

512 Divisions:
Casio: 7,354,200,000
Sharp: 7,354,157,599
|Es|<= 796.7147252
7,354,156,803 - 7,354,158,396
Looks like the first 6 significant figures can be counted on with rounding: 735416. The Casio could of gone for another significant figure, but it still returns the correct answer.

Note: that |Es| gives the maximum possible error for a function using the Simpson rule given the number of divisions, and it's 4th derivative; not the actual error.

In addition it seems to automatically vary the number of divisions depending on the function and it's interval, so certain integrations will go faster. This is something Sharp needs themselves if they are sticking with the Simpson method (both the error and auto interval logic).

I guess with the ES and now EX series stealing the show from the MS with it's better integration algorithm (Gauss-Kronrod?, it's above my current math ability) and nicer display it probably doesn't matter anymore, but this is a rather impressive feat IMO. I also like that the MS is still the only series with the "Copy-Replay" function, or the ability to scroll up several functions ago and copy that function and all others that proceed for editing.

Look at me blabbing on about the Casio MS series on a post about a new Sharp.

Back to the Sharp:

I still prefer my Sharp EL-W516X over the Casio fx-115es Plus (only by a tiny bit, as I much prefer the equation solver, Integration and differentiation on the Casio), but mostly because of these 3 reasons:
1) The ability to save your Writeview history when powering off.

2) Being able to store relatively big equations in 4 memories and easily recall them (eg the |Es| error tests were done on the Sharp, since I can store both the 4th derivative maximum, the |Es| function to make use of that, as well as the Summation version of the function (though I could just of used the built in Sharp one!)).

3) Great Summation functionality, since you can specify the interval size (algebraically as well).

If it was the Casio fx-991ex instead, well, I'd probably go with that for it's much better display and faster processing, but I would miss terribly the ability to save my calculation history or formulas.

[Pjwum]

(11-13-2019 11:43 PM)rprosperi Wrote:  Though probably just perfect for any integral your daughter will encounter... and likely anyone else that doesn't seek pathological equations to integrate. .

I checked and yes, it is an EL-W506X and it says WriteView right over the LCD.

Let me come back to its calculus capabilities. I repeated the integral and these are the numbers:
Casio fx-991DE: 5.963938092E+91
Prime (Handheld): 5.96393809188E+91
Sharp W506X: 7.466216848E+91

Meanwhile I learned you may specify n as an option when entering the formula.

But does its auto mode of only 100 Simpson intervals really affect everyday calculations? Let us assume some average physics teacher in high school proposing this task: Calculate the energy needed to bring Tesla's starman (1000 kg) one light year away from Earth!
Instead of finding the antiderivative you try to solve the integral(rE, 1 ly, G*mE*1000kg/r^2) numerically. In auto mode without specifying n you will then find (kg*m^2/s^2):
Casio fx-991DE: 6.251161691E+13
Prime (Handheld): 6.25116169124E+13
Sharp W506X: 1.547252475E+20

[rprosperi]

(11-14-2019 06:35 PM)Pjwum Wrote:  

(11-13-2019 11:43 PM)rprosperi Wrote:  Though probably just perfect for any integral your daughter will encounter... and likely anyone else that doesn't seek pathological equations to integrate. .

I checked and yes, it is an EL-W506X and it says WriteView right over the LCD.

Let me come back to its calculus capabilities. I repeated the integral and these are the numbers:
Casio fx-991DE: 5.963938092E+91
Prime (Handheld): 5.96393809188E+91
Sharp W506X: 7.466216848E+91

Meanwhile I learned you may specify n as an option when entering the formula.

But does its auto mode of only 100 Simpson intervals really affect everyday calculations? Let us assume some average physics teacher in high school proposing this task: Calculate the energy needed to bring Tesla's starman (1000 kg) one light year away from Earth!
Instead of finding the antiderivative you try to solve the integral(rE, 1 ly, G*mE*1000kg/r^2) numerically. In auto mode without specifying n you will then find (kg*m^2/s^2):
Casio fx-991DE: 6.251161691E+13
Prime (Handheld): 6.25116169124E+13
Sharp W506X: 1.547252475E+20

Gee, that's only off by a factor of ~2.5E06; what's 1.5E20 kg*m^2/s^2 among friends?

Seriously, that is surprisingly poor, so you've made a really good point here, though I still doubt she will get an assignment like that in High School.

If you set n manually, is it retained for future integrals, or is it reset to the default for each integral/equation you try to solve?

From curiosity, do you happen to know how many intervals the fx-991DE and Prime used to achieve essentially the same result?

[Mjim]

I tried this myself, but I kept getting different results. I downloaded Xcas to my PC (https://www-fourier.ujf-grenoble.fr/~parisse/giac.html I think the same engine behind the HP Prime):

Using: G=6.67430*10^-11, rE = 6.371*10^6, mE = 5.972*10^24, 1ly (in metres) = 299,792,458*3600*24*365.25
C = G*mE*1000 = 3.98589*10^17

E = integrate(C/r^2, rE, 1ly):
Wolfram (only gave 6 significant figures): 6.25631*10^10
Xcas: 6.25630506563*10^10
Casio fx-9750GII: 6.256305066*10^10
Casio fx-570MS (upgraded temporarily from a fx-82MS): Throws math error.
Sharp EL-W516X:
-Default divisions: 1.54840203*10^17
-1024 divisions: 6.694153651*10^10
-4096 divisions: 6.258289041*10^10
-32768 divisions: 6.251558833*10^10 (This took a very...very long time)

Not sure if these results are right; might of made a mistake with some units somewhere.

The Sharp is way off, part of it could be internal digit accuracy. If you move the constant C outside of the integral the Casio fx-9750GII will give 29390.80513 as an answer which will actually increase if we decrease the distance to 1 light second where it pops back up to 6.1233*10^10. The Xcas result is perfect either way, so perhaps the Prime will be similar?

The Casio fx-82MS error algorithm basically told us to go away, which is a better outcome since there is no way it could give a good approximation using the Simpson algorithm, if even the Sharp at 1024 divisions (512 more then the max on the Casio MS), couldn't even get a single significant figure down.

Good example for showing the weakness in the Simpson Integration algorithm. I have to agree that I don't trust the Sharp for integration, but to be fair, any calculator using the Simpson algorithm will likely have the same issue; the Casio 570MS just clearly recognizes when it won't be able to deliver a good result and throws a math error, but any other calculator with the same Simpson Algorithm will probably suffer similarly.

BTW, with this integration example, 1/r^p is convergent if p > 1; so since p = 2 we know that this function is convergent. The energy needed to offset earth's gravitational influence is essentially a fixed value beyond a certain distance. In any case, this means there isn't much difference between 1 light day and 1 light year in terms of energy required, which makes sense as earths gravity is pretty much negligible after traveling 173 AU or 173 times the distance from earth to the sun).

[klesl]

According to the UG the Casio fx-991EX uses Gauss-Kronrod method.

[lrdheat]

Another difference between the CASIO fx-991EX and TI-30X Pro MathPrint (European edition of the 36X Pro of the U.S) is that the CASIO, while being able to handle some integrals where a function is undefined at an endpoint/endpoints, cannot deal with a function that is undefined at some point within the interval being considered. The TI’s can handle these situations. The work around on the CASIO is to divide integral into 2 integrals, and, if necessary, integrate each integral from a 1E-12 offset from the offending interval start and/or end points.

[Mjim]

(11-15-2019 10:57 PM)lrdheat Wrote:  Another difference between the CASIO fx-991EX and TI-30X Pro MathPrint (European edition of the 36X Pro of the U.S) is that the CASIO, while being able to handle some integrals where a function is undefined at an endpoint/endpoints, cannot deal with a function that is undefined at some point within the interval being considered. The TI’s can handle these situations. The work around on the CASIO is to divide integral into 2 integrals, and, if necessary, integrate each integral from a 1E-12 offset from the offending interval start and/or end points.

That's handy that the TI-30X/36X Pro does that; what kind of answer would it give if say you tried to integrate 1/x from [0,1] ? (an improper integral: https://socratic.org/questions/how-do-yo...-converges)

I've thought about whether the Ti-36X Pro might be a better fit than the Sharp, since I have heard that it can store it's history as well. It's a little more limited with expressions though (maximum expression length is double on the Sharp (159 characters on the Sharp vs 80 on the TI-36X Pro). Not a fan of the design and the display contrast (though I haven't seen it in person, so perhaps it isn't as bad as it looks on the videos).

The integration seems faster from the few video's I've seen, but I'm not sure what integration method it is using (is it Gauss-Kronrod like the Casio?).

It may just be I'm a bit biased against TI; in the US I'm guessing that is the default brand of calculator that students grow up with, where over here Casio was what every student learns to use. I tried to be 'edgy' in my youth and bought a Sharp calculator in school (after a google I'm certain it was the EL-556G), and bought myself what I think was the Sharp EL-5120 programmable for post-school studies; though I wasn't much of a fan of that one (probably didn't know how to use it properly). It's probably why I have a bit of soft spot for Sharp even though Casio outclasses them in many other areas.

[lrdheat]

The TI 30X Pro MathPrint is much faster than the 36X Pro, rather identical to the 991EX in speed and integration answers...I’m guessing that the TI is using the same integration method as the CASIO. Both the CASIO and TI correctly throw errors with the integral that you asked about. The 30X can accept much longer equations than the 36X Pro. I did not have the patience to test how lengthy an expression is possible, but much better than the frustratingly small capacity of the 36X Pro. I really like the 30X. I like how it uses a default epsilon of 1E-5 in it’s integration and differentiation operations, but in the math menu, allows the user to choose a much finer epsilon if desired...I can key in 1E-9, for example, or anything else that I might desire.

[ijabbott]

(11-16-2019 01:23 AM)Mjim Wrote:  I've thought about whether the Ti-36X Pro might be a better fit than the Sharp, since I have heard that it can store it's history as well. It's a little more limited with expressions though (maximum expression length is double on the Sharp (159 characters on the Sharp vs 80 on the TI-36X Pro). Not a fan of the design and the display contrast (though I haven't seen it in person, so perhaps it isn't as bad as it looks on the videos).

I wasn't a fan of the silver keys on the TI-36X Pro / TI-30X Pro MultiView, but thankfully, those have been replaced with dark grey keys on the TI-30X Pro MathPrint (and on its fewer-featured sibling, the TI-30X Plus MathPrint). The display is also double the resolution (mainly to improve the fonts, rather the number of displayed characters), and the pixel colour has changed from blue to black.

(11-16-2019 06:14 AM)lrdheat Wrote:  The 30X can accept much longer equations than the 36X Pro. I did not have the patience to test how lengthy an expression is possible, but much better than the frustratingly small capacity of the 36X Pro.

I got 101 symbols on the entry line of the TI-30X Pro MathPrint, in both MATHPRINT and CLASSIC display modes. A symbol is a numeric character, an operator, a parenthesis or a function with its opening parenthesis (e.g. "sin(" is one symbol).

In MATHPRINT mode, some parentheses may be added automatically and hidden from view, but still count towards the number of symbols on the line. For example "\(e^1\)" is stored as three symbols: "e^(", "1", ")". Fractions such as "\(\frac{1}{2}\)" are stored with added, hidden parentheses: "(", "1", "/", "2", ")".

[Mjim]

(11-16-2019 06:14 AM)lrdheat Wrote:  The TI 30X Pro MathPrint is much faster than the 36X Pro, rather identical to the 991EX in speed and integration answers...I’m guessing that the TI is using the same integration method as the CASIO. Both the CASIO and TI correctly throw errors with the integral that you asked about. The 30X can accept much longer equations than the 36X Pro. I did not have the patience to test how lengthy an expression is possible, but much better than the frustratingly small capacity of the 36X Pro. I really like the 30X. I like how it uses a default epsilon of 1E-5 in it’s integration and differentiation operations, but in the math menu, allows the user to choose a much finer epsilon if desired...I can key in 1E-9, for example, or anything else that I might desire.

Never saw the TI-30X Pro MathPrint until today. Very much like the design and display...but it doesn't seem to exist outside of Germany, and what is available on ebay is expensive. In fact, I couldn't find a single review on it. It's a very nice looking TI calculator, but I wouldn't even believe it existed if not for the emulator and PDF manual I downloaded for it.

Looks like it has a pretty decent sized solar cell. I did a pretty rough test using my cellphone sensor, but the Sharp EL-W516X needed about 350 lux to work properly with indoor lighting or about 250 lux with overcast sky lighting (The measurement I did was pretty rough, so the difference may not mean anything). Would love to see more solar powered calculator reviews cover how well they do under different light situations.

TI-30X Pro MathPrint emulator impressions:
I'm not used to Texas Instruments calculators, so at first glance I'm not sure if I like the button layout; for example I like having a dedicated x^-1 key. On the other hand I do like how they did the inverse trig functions; a double tap to switch between both, nice design, much better than having them require the shift key. It's also great that there is a dedicated button for x (although on the sharp it's fairly easy compared to the Casio as well, since you can just double tap RCL to pick x).

Integration seems to work accurately like Casio. I got the same answer as the Casio by plugging in that energy equation a few posts above, and it wasn't too slow (fx-9750GII is much faster, but that isn't unusual comparing a solar powered scientific calculator vs a graphing one). Nice to know I can trust the integration on this.

Differentiation seems slightly better than the Sharp EL-W516X; but isn't as good as the Casio fx-991ex and suffers by losing digits (like the Sharp) when you specify smaller epsilons:

d/dx(e^(x^3),x,x=6):

Casio fx-991EX:
6.934766564*10^95 (default epsilon, but accurate for all displayed digits)

Sharp EL-W516X:
6.93477882*10^95 (default epsilon)
6.93568*10^95 (epsilon = 1*10^-10)

TI-30X Pro MathPrint:
6.934767925*10^95 (default epsilon)
6.93475*10^95 (epsilon = 1*10^-10)

It's kind of annoying that it loses digits by specifying a smaller epsilon, but I guess the TI-30X Pro MathPrint still holds it accuracy better than the Sharp.

Numerical solver isn't quite as nice as the Casio, for example:

e^2x - 3 = ln(2x + 1)

You can see there will be a problem when x = -0.5 for the log on the right. Both the TI & Sharp will throw up error messages when using x=-0.5 (though the TI will at least let you know it was a bad guess rather than Sharp's non informative ERROR 02). The Casio fx-991ex somehow figures out a way to work around the bad guess and will solve the problem anyway. The solutions returned are pretty accurate for all 3 calculators (mostly differences in the hidden digits), but Sharp is the least flexible only solving for x and requiring everything to be on the left side.

Table function is good and seems to work the same as the new Sharp EL-W506T; you specify a starting point and interval, but can scroll forever in either direction.

Calculation History seems comparable to the Sharp as well, but showing the results of previous equations on the same screen is so much more useful (Seems silly that Sharp wastes all that screen space by only ever showing the current problem you are working on and not the previous calculation history).

Tried typing in that formula in the Expression mode, but I couldn't fit the last 1/3rd of the equation in. The TI-30X emulator didn't actually bring up a buffer full message, just kind of stopped me typing any more of the equation.

That "set op" function seems to work the same as the equation storage on the Sharp; so I guess between that gives effectively 5 equation memories (set op, num-solv, expr-eval, and the 2xTable functions (f(x) & g(x)) ), although I'm not sure (except from "set op") if you can copy them to the main display.

That Data editor looks pretty good as well, though I got stuck when trying to enter an equation in on of the columns (wanted to see if I could save more equations there!); the sequence operation worked a charm though.

I did try to integrate sin(x)/x on the interval [0, pi/2] and you are quite right about handling undefined intervals as when x=0. The TI-30X Pro mathprint can deal with the division by zero no problems and can even handle a wider interval such as [-pi/4, pi/2], where the division by zero isn't at the end points. I was surprised that the Casio fx-991ex couldn't deal with this, despite using a better integration algorithm than the Sharp (the sharp did indeed fail as well with this).