# include <stdio.h>
# include <math.h>
//
//  Replace ? by a declaration for f.
//
double midpoint ( ?, int n, double a, double b );
double poly ( double x );
double wave ( double x );

int main ( )
{
  double a;
  double b;
  int n;
  double q;
//
//  Replace ? by poly.
//
  n = 10;
  a = 0.0;
  b = 4.0;
  q = midpoint ( ?, n, a, b );
  printf ( "  Estimated integral for poly(x) is %g\n", q );
//
//  Replace ? by wave
//
  n = 10;
  a = 1.0;
  b = 3.0;
  q = midpoint ( ?, n, a, b );
  printf ( "  Estimated integral for wave(x) is %g\n", q );

  return 0;
}
//
//  Replace ? by a declaration for f.
//
double midpoint ( ?, int n, double a, double b )
{
  double ai;
  double bi;
  double dx;
  int i;
  double q;
  double x;

  dx = ( b - a ) / n;
  
  q = 0;

  for ( i = 0; i < n; i++ )
  {
    ai = a + i         * dx;
    bi = a + ( i + 1 ) * dx;
    x = ( ai + bi ) / 2.0;
//
//  Replace ? by the name "f"
//
    q = q + dx * ? ( x );
  }
  return q;
}

double poly ( double x )
{
  double value;

  value = ( x + 1 ) * ( x - 1 ) * ( x - 1 ) * ( 4 - x );

  return value;
}

double wave ( double x )
{
  double value;

  value = 1.0 + cos ( x - 2.0 );

  return value;
}