Exercise 1.29: Simpson’s Rule is a more accurate
method of numerical integration than the method illustrated above.  Using
Simpson’s Rule, the integral of a function 
  f
 between 
  a
 and 
  b
 is
approximated as


  
    h
    3
  
  (
  
    y
    0
  
  +
  
    4
    
      y
      1
    
  
  +
  
    2
    
      y
      2
    
  
  +
  
    4
    
      y
      3
    
  
  +
  
    2
    
      y
      4
    
  
  +
  ⋯
  +
  
    2
    
      y
      
        n
        −
        2
      
    
  
  +
  
    4
    
      y
      
        n
        −
        1
      
    
    +
    
      y
      n
    
    )
    ,
  


where 
  
    h
    =
    (
    b
    −
    a
    )
    
      /
    
    n
  
, for some even integer 
  n
, and

  
    y
    k
  
  =
  
    f
    (
    a
    +
    k
    h
    )
  
.  (Increasing 
  n
 increases the
accuracy of the approximation.)  Define a procedure that takes as arguments

  f
, 
  a
, 
  b
, and 
  n
 and returns the value of the integral, computed
using Simpson’s Rule.  Use your procedure to integrate cube between 0
and 1 (with 
  
    n
    =
    100
  
 and 
  
    n
    =
    1000
  
), and compare the results to those of
the integral procedure shown above.