Solve with integrating an implicit function

[parisse]

I don't believe there is a simple way to do that, since you don't have control on evaluation like in RPN.
Here is a not too complicated way in Xcas, therefore it should also work in CAS :
1/ first define the implict function
f(x):=fsolve(y^5+y=x,y=0..2)[0]
2/ then the integral g(t):=romberg('f(x)',x,0,t)
3/ Check that g(0.7) and g(1) have opposite sign.
4/ then solve using Newton method
h(t):=t-(g(t)-1/3)/f(t)
h(h(h(1.0))) and h(h(h(h(1.0)))) are almost identical.