Create the function which integrates using Simpon's rule with adaptive quadrature. Verify and show the code against 3 different functions. Two you must be able to integrate by hand and other is error function erf(z). For known integral you can do by hand determine values of n for the older Simpson function (with fixed n) versus adaptive quadrature. Show difference in number of partitions for different versions for integrating sin(1/x) from 0.1 to 8 for accuracy to 10^(-8).