These two SS 6179 Companions meet the best known Mathcad numerical integrators.
Carlos ∫Adaptive(f,a,b,N,ε) supports ∞ limits and/or singular end points
from wisely input the limits of the integrator.
Either Romberg-Simpson version will plot on the canvas.
Native Simpson is only for Classroom or as applicable.
Functions may look naive to integrate but Simpson may fail.
Always cross check as possible. Have Wolfram Alpha near hand.
Accuracy of integration is specified 4 decimals in some Standards.

Jean

Integral COMPANION Adaptive Romberg-Simpson(f,a,b,n).sm (46 KiB) downloaded 80 time(s).

... infinitesimal added/exemplified.
Most useful for discontinuous functions [typical b_spline].
If you have hard to manage project, welcome to propose.

Integral COMPANION Adaptive Romberg-Simpson(f,a,b,n).sm (142 KiB) downloaded 64 time(s).

Wrote

... infinitesimal added/exemplified.
Most useful for discontinuous functions [typical b_spline].
If you have hard to manage project, welcome to propose.

... slight shadow in context last Corn Thermies ... corrected ∫

Integral COMPANION Adaptive Romberg-Simpson(f,a,b,n) Copy.sm (142 KiB) downloaded 66 time(s).