# Adaptive Quadrature# # # We test some of our numerical quadrature rules. We first define some# data points.> restart; Digits := 10; with(student):                             Digits := 10> f := sin(1/x);> plot(f,x=.1..10);                            f := sin(1/x)# Apply the Composite Simpson's  rule with a number of subintervals and# compare with the "exact" value Maple computes.> int(f,x=.1..10);                             2.735148231> evalf(simpson(f,x=.1..10,2));> evalf(simpson(f,x=.1..10,4));> evalf(simpson(f,x=.1..10,8));> evalf(simpson(f,x=.1..10,16));> evalf(simpson(f,x=.1..10,32));> evalf(simpson(f,x=.1..10,64));> evalf(simpson(f,x=.1..10,128));> evalf(simpson(f,x=.1..10,256));                             .5654965345                             1.644977754                             2.399717067                             2.806832245                             2.789905488                             2.625176290                             2.684313127                             2.736193244>