(define (product term a next b)
  (cond
    ((> a b) 1)
    (else (* (term a) (product term (next a) next b)))))

(define (i-product term a next b)
  (cond ((> a b) null)
      (else
       (define (iter a result)
         (cond ((> a b) result)
               (else (iter (next a) (* (term a) result)))))
       (iter a 1))))

(define (identity x) x)
(define (inc x) (+ 1 x))
(define (multiply-integers a b) (i-product identity a inc b))

(define (square x) (* x x))
(define (compute-pi steps)
  (define (next n) (+ n 2.0))
  (* 8.0 (* steps 2) (/ (i-product square 4.0 next (* (- steps 1) 2))
              (i-product square 3.0 next (* steps 2)))))

(define (factorial n)
  (define (next n) (+ n 1))
  (i-product identity 1 next n))

(define (product term a next b)
  (if (> a b)
      1
      (* (term a) (product term (next a) next b))))

(define (i-product term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a) (* (term a) result))))
  (iter a 1))

(define (compute-pi steps)
  (define (next n) (+ n 2))
  (* 8.0 (* steps 2) (/ (i-product square 4 next (* (- steps 1) 2))
                        (i-product square 3 next (* steps 2)))))