HP42s first major program (Double Integral) Best way to approach?

[Thomas Okken]

The data structures used by SOLVE and INTEG are static, which is why those functions don't nest. They are separate from each other, so you can solve a function that uses INTEG or integrate a function that uses SOLVE.

I'm guessing HP didn't bother to make SOLVE and INTEG nestable because it would have been too slow to be useful anyway. In Free42 or the DM42, it would make more sense, but it would require additions to the instruction set since you would have to be able to explicitly distinguish between PGMSLV and PGMINT resetting the existing solver or integrator instance and creating new nested instances.