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):=
   (B-A)/N/3 * (apply(F,[A])+apply(F,[B]) +
   4*SUM(apply(F,[A+(B-A)/N*(2*I-1)]),I,1,N/2)
 + 2*SUM(apply(F,[A+(B-A)/N*(2*I)]),I,1,(N-2)/2))$