You programmed SYMBOLIC integration on a TI-82 but couldn't do it by hand? Are you sure you are remembering that right? Symbol integration is non-trivial.
Almost certainly not. It happened over 20 years ago so my memory is fuzzy, but I’d guess I still had to tell it which formula I wanted to integrate with. So to study I just had to be able to identify the correct formula. You might argue that’s the not much harder than by hand, but I was exceedingly lazy (still am, but now married with kids so it’s buried deep haha).