1 (define (sum term a next b)
2   (if (> a b)
3       0
4       (+ (term a)
5 	 (sum term (next a) next b))))
6 
7 ;; (define (simpsons-rule f a b n)
8 ;;   (let ((h (/ (- b a) n)))
9 ;;     (define (running-sum k)
10 ;;       (let ((akh (+ a (* k h))))
11 ;; 	(if (= k n) 
12 ;; 	    (f akh)
13 ;; 	    (+ (cond ((= k 0) (f akh))
14 ;; 		     ((even? k) (* 2 (f akh)))
15 ;; 		     ((odd? k) (* 4 (f akh))))
16 ;; 	       (running-sum (+ k 1))))))
17 ;;     (* (/ h 3)
18 ;;        (running-sum 0))))
19 
20 (define (simpsons-rule f a b n)
21   (let ((h (/ (- b a) n)))
22     (define (simpsons-term k)
23       (let ((akh (+ a (* k h))))
24 	(* (f akh)
25 	   (cond ((or (= k 0) (= k n)) 1)
26 		 ((odd? k) 4)
27 		 ((even? k) 2)))))
28     (* (/ h 3)
29        (sum simpsons-term 0 1+ n))))
30 
31 
32 (define (test-case actual expected)
33   (load-option 'format)
34   (newline)
35   (format #t "Actual: ~A Expected: ~A" actual expected))
36 
37 (define (cube x) (* x x x))
38 
39 (test-case (simpsons-rule cube 0.0 1.0 5) 0.25)
40 (test-case (simpsons-rule cube 0.0 1.0 10) 0.25)
41 (test-case (simpsons-rule cube 0.0 1.0 100) 0.25)
42