(define (estimate-integral p x1 x2 y1 y2 times)
  (let ((rect-area (* (- x2 x1) (- y2 y1)))
        (ratio (monte-carlo times (lambda () (exp p x1 x2 y1 y2)))))
    (* rect-area ratio)))

(define (exp p x1 x2 y1 y2)
  (let ((random-x (random-in-range x1 x2))
        (random-y (random-in-range y1 y2)))
    (p (make-point random-x random-y))))
    
(define (in-circle? circle)
  (lambda (point)
    (let ((circle-x (caar circle))
          (circle-y (cadar circle))
          (radius (cadr circle))
          (test-x (car point))
          (test-y (cadr point)))
      (<= (+ (square (- test-x circle-x)) (square (- test-y circle-y))) (square radius)))))
        
(define (make-circle center radius)
  (list center radius))

(define (make-point x y)
  (list x y))

(define (square x)
  (* x x))

(define (monte-carlo trials experiment)
  (define (iter trials-remaining trials-passed)
    (cond ((= trials-remaining 0)
           (/ trials-passed trials))
          ((experiment)
           (iter (- trials-remaining 1) (+ trials-passed 1)))
          (else
           (iter (- trials-remaining 1) trials-passed))))
  (iter trials 0))

(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random range))))


(define (estimate-pi)
  (let ((radius 5.0)
        (times 1000000)
        (x 0)
        (y 0))
    (let ((circle (make-circle (make-point x y) radius)))
      (let ((area (estimate-integral (in-circle? circle) -5 5 -5 5 times)))
        (/ area (square radius))))))

(estimate-pi)