simpson's 1-3rd rule Algorithm

In numerical analysis, Simpson's rule is a method for numerical integration, the numerical estimation of definite integrals. However, Johannes Kepler used like formulas over 100 years prior, and for this reason, the method is sometimes named Kepler's rule, or Keplersche Fassregel (Kepler's barrel rule) in German.

simpson's 1-3rd rule source code, pseudocode and analysis