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(define (cube x) (* x x x))
(define (inc x) (+ x 1))
(define (sum term a next b)
(if (> a b)
0
(+ (term a)
(sum term (next a) next b))))
(define (integral f a b dx)
(define (add-dx x) (+ x dx))
(* (sum f (+ a (/ dx 2.0)) add-dx b)
dx))
(define (integral-simpson f a b n)
(define h (/ (- b a) n))
(define (y k) (f (+ a (* h k))))
(define (mul k) (if (or (= 0 k) (= n k)) 1
(if (even? k) 2 4)))
(define (term k) (* (mul k) (y k)))
(* (/ h 3.0)
(sum term 0 inc n)))
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