Adaptive Simpson's Rule

The adaptive Simpson's rule for quadrature uses the two subroutines "Simpson" and "Adapt."The program is "recursive".There is no brake available if something goes wrong, i.e. if a pathological "bad" function is thrown it's way it may proceed on a slippery path of infinite recursion.

Mathematica Subroutines (Adaptive Simpson's Rule).

Execute the following Mathematica subroutine, which is the "long version" of the subroutine we have been using previously.