;; define a function that takes n and returns n^2 + n + 1:
(define (f n) (+ (* n n) n 1))

;; test 1:
(f 2)
;; expected result:
7

;; test 2:
(f -2)
;; expected result:
3

;; Exercise 2.2.5 
;; http://www.htdp.org/2003-09-26/Book/curriculum-Z-H-5.html#node_sec_2.2
;; write the expressions and the tests, then test them. 

;; Programs for word problems 

;; define constant PI
(define PI 3.14)

;;;;;;;;;;; Function definition with a contract, etc. ;;;;;;;;;;;;;;

;; Contract: area-of-disk : number -> number

;; Example: (area-of-disk 1) produces 3.14

;; Purpose: to compute the area of a disk whose radius is r

(define (area-of-disk r) 
  (* PI (* r r)))

(area-of-disk 1)
;; Test
;; expected value 3.14
3.14

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; Contract: area-of-ring : number number  ->  number

;; Purpose: to compute the area of a ring whose radius is
;; outer and whose hole has a radius of inner

;; Example: (area-of-ring 5 3) should produce 50.24

; Definition: [the function written in Scheme]
(define (area-of-ring outer inner)
  (- (area-of-disk outer)
     (area-of-disk inner)))
  
;; Tests:
(area-of-ring 5 3) 
;; expected value
50.24

;; Exercise 2.3.1
;; http://www.htdp.org/2003-09-26/Book/curriculum-Z-H-5.html#node_sec_2.3

;; Exercise 2.3.3