File: simpsn.mac

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traprule(f,a,b,n):=
   (b-a)/n * ((apply(f,[b])+apply(f,[a]))/2 +
   sum(apply(f,[a+(b-a)/n*i]),i,1,n-1))$

simpson(f,a,b,n):=
    block ([nn : ceiling (n / 2)],
   (1/6)*(b-a)/nn * (apply(f,[a])+apply(f,[b]) +
   4*sum(apply(f,[a+(b-a)/(2*nn)*(2*i-1)]),i,1,nn)
 + 2*sum(apply(f,[a+(b-a)/(2*nn)*(2*i)]),i,1,nn-1)))$