! ---------------------------------------------
! Example program
! subroutine called with a function as argument
! ---------------------------------------------
program test
  implicit none
  real(kind(1.d0)):: pi,res,step,a,b
  intrinsic:: dsin ! a double precision version on sin()
  pi   = 4.d0*atan(1.d0)
  a    = 0.d0
  b    = pi
  step = 0.1d0 
  do
     call integral(dsin,a,b,step,res) 
     write(*,'("step ",es8.2,"    integral ",es25.15)') step,res
     step = 0.1d0*step 
     if(step<1.d-7) exit 
  end do
end program test

! ------------------------------
! computes the definite integral
! of f(x) from a to b with step dx
! as a Riemann sum
! ------------------------------
subroutine integral(f,a,b,dx,res)
   implicit none 
   real(kind(1.d0)), intent(in):: a,b,dx
   real(kind(1.d0)), intent(out):: res
   real(kind(1.d0)), external:: f 
   real(kind(1.d0)):: x
   res = 0.d0
   x   = a
   do 
      res = res + f(x)
      x = x + dx
      if(x>b) exit
   end do
   res = dx*res
 end subroutine integral