#include<iostream.h>

/* computes the sum 1*(0*0) + 4*(1*1) + 2*(2*2) + 4*(3*3) + 2*(4*4) +
    ... + 2*(num-2)*(num-2) + 4*(num-1)*(num-1) + 1*(num*num), where
   num is a positive even integer.  (This sort of sum comes up in
   Simpson's rule in calculus.)  If i is a counter variable going from
   0 to num, then the general term in the sum is of the form coeff*i*i, 
   where the coefficient coeff is determined by this rule:
      if i is odd, then coeff = 4
      if i is 0 or i is num, then coeff = 1
      if i is even, and not 0 or num, then coeff = 2 */


void main() {

  int num=10, sum=0, i, coeff;

  for (i=0; i<=num; i++){

    if (i%2) coeff = 4;
    else if (i==0 || i==num) coeff = 1;
    else coeff = 2;

    sum += coeff * i*i;
  }
  cout << "The sum is "<< sum <<".\n";
}