(define (inc n) (+ n 1))

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

(define (simpson f a b n)
  (simpson-h f a b n (/ (- b a) n)))

(define (simpson-h f a b n h)
  (define (y k)
    (f (+ a (* k h))))
  (define (term k)
    (cond ((= k n)  (y k))
          ((= k 0)  (y k))
          ((odd? k) (* 4 (y k)))
          (else     (* 2 (y k)))))
  (* (/ h 3)
     (sum term 0 inc n)))