This visit compares some common numerical integrators wrt accuracy/speed.
The Smath Romberg is grand champion ... feature suggestion

Read more:

1. Simpson,
2. Simpson-Richardson,
3. Adaptive [singular],
4. Romberg [singular].

In this document, we yardstick Mathcad 11 [well reputed high class integrators].
More integrators may be found from literature.

Enjoy/comment/suggest ...

Jean

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