(define (sum-integers-1 a b)
	(if (> a b)
	    0
	    (+ a (sum-integers-1 (+ a 1) b))))

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

(define (inc n) (+ n 1))
(define (cube x) (* x x x))

(define (sum-cubes a b)
	(sum cube a inc b))

(define (sum-integers a b)
	(define (self x) x)
	(sum self a inc b))

(define (sgn x)
   (define (foo n)
     (* (/ x (sqrt (* x x))) n))
   foo)

(define (pi-approx b)
	(define (term_pi x) (/ 1.0 x))
	(define (next_pi x) (- ((sgn x) (+ 2 (abs x)) ) ))
	(* 4 (sum term_pi 1 next_pi b)))

(define (integral f a b dx)
	(define (add-dx x) (+ x dx))
	(* dx
	   (sum f (+ a (/ dx 2)) add-dx b))