# include <stdlib.h>
# include <stdio.h>
# include <math.h>

int main ( );
double w ( double x );

int main ( )
{
  double a;
  double b;
  int i;
  int n = 1000;
  double q;
  double x;

  q = 0.0;
  for ( i = 0; i < n; i++ )
  {
    a = ( ( n - i     ) * 1.0 + ( i     ) * 100.0 ) / n;
    b = ( ( n - i - 1 ) * 1.0 + ( i + 1 ) * 100.0 ) / n;
    x = 0.5 * ( a + b );
    q = q + ( b - a ) * w ( x );
  }
  printf ( "Q = %g\n", q );

  return 0;
}
double w ( double x )
{
  double a;
  double b;
  int it;
  double tol = 1.0E-10;
  double value;

  value = x + log ( x );

  it = 0;

  while ( 1 )
  {
    if ( 100 < it )
    {
      break;
    }

    if ( fabs ( ( x - value * exp ( value ) ) ) < 
      tol * fabs ( ( value + 1.0 ) * exp ( value ) ) )
    {
      break;
    }
    a = value * exp ( value ) - x;
    b = ( value + 1.0 ) * exp ( value ) 
      - ( value + 2.0 ) * ( value * exp ( value ) - x ) / ( 2.0 * value + 2.0 );
    value = value - a / b;
    it = it + 1;
  }
  return value;
}