program prog032
      implicit real*8 (a-h,o-z)
      external f1
      a=0.0d0
      b=1.0d0
      exa=2.0d0
c
      do n=10,100,10
         call chutenf(f1,a,b,n,sum)
         dx=(b-a)/n
         err=abs(sum-exa)
         write( *,800) n, dx, sum, exa, err, err/dx/dx
         write(16,800) n, dx, sum, exa, err, err/dx/dx
      enddo
 800  format(1x,i4,5(1x,f10.7))
c
      end
c **********************************************************************
      subroutine chutenf(FUNC,a,b,n,sum)
c **********************************************************************
c
c     This subroutine calculate the integral
c       sum = integral_a^b FUNC(x)
c     by using the Mid-Point formula.
c
      implicit real*8 (a-h,o-z)
      external FUNC
c
      sum = 0.0D0
      dx = (b - a)/n
      do i = 1,n
         x  = a + (i - 0.5D0)*dx
         sum = sum + FUNC(x)
      end do
      sum = sum*dx
c
      end
c **********************************************************************
      function f1(x)
c **********************************************************************
c     function f1(x)=pi*sin(pi*x)
c **********************************************************************
      implicit real*8 (a-h,o-z)
c
      pi=4*atan(1.0d0)
      f1=pi*sin(pi*x)
c
      end