#lang sicp
; (define (cube x) (* x x x))

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
         (sum term (next a) next b))))

(define (inc x) (+ 1 x))

(define (simpson f a b n)
  (define h (/ (- b a) n))
  (define (add-h x) (+ x h))
  (define (term i)
    (cond ((= i 0) (f a))
          ((= i n) (f b))
          ((even? i) (* 2 (f (+ a (* i h)))))
          (else      (* 4 (f (+ a (* i h)))))))
  (* h
     (/ 1.0 3)
     (sum term 0 inc n)))