Problem 55200. Scorer's Function

This is my favorite of your problems so far, Dyuman. My inability to read the manual carefully led me to try several approaches, which is never bad, and I kludged two of them together in solution 8748010. It helped to finally remember *my own problem*, which--to avoid spoilers--I won't cite.

Thanks Chris!
I was actually waiting for you to realize it haha.

The original plan was to use the explicit formula to check if the problem could be solved or not, which looks easy on paper, however, was not so easy to implement numerically.

And then it clicked me!

To me it's interesting that if I had read the manual correctly, I wouldn't have thought about numerical evaluation of highly oscillating integrals, the method of stationary phase, the method of steepest descent, numerical solution of an ODE, hypergeometric functions, and more. There's a lesson in there about the value of mistakes.