program teach03
      implicit real*8 (a-h,o-z)
c
c     This program calculate the integral
c       sum = integral_a^b sin(x) dx
c     by using the Mid-Point formula.
c
      write(*,*) 'n, a, b = ?'
      read(*,*)   n, a, b
      write(*,*) 'n = ', n,' a = ',a,' b = ',b
      open(16,file='teach03.dat')
c
      sum = 0.0d0
      dx = (b - a)/n
c
      do i = 1, n
         x = a + (i - 0.5d0)*dx
         sum = sum + f(x)
         write(16,800) x, f(x)
 800  format(2(1x,f12.5))
      end do
         sum = sum*dx
c
      exa=-(cos(b)-cos(a))
      write(*,*) 'Sum    = ',sum
      write(*,*) 'Exact  = ',exa
      stop
      end
c **********************************************************************
      function f(x)
c **********************************************************************
      implicit real*8 (a-h,o-z)
      f = sin(x)
      end