! While passing procedures as arguments a few things should be noted:
!
!  (1) Functions that are declared in the main program after 'contains'
!      cannot be passed as arguments
!  (2) Functions declared outside of the main program have to be declared
!      as external in the main program

! Module
module my_mod
contains
  function integrate(fx, a, b, n)
    implicit none
    real, external :: fx  ! external here is optional but recommended
    real :: integrate, a, b, delta, total
    integer :: n, i
    delta = (b - a) / real (n) 
    total = 0.0
    do i = 1, n
       total = total + (fx (a + (i-1) * delta + delta / 2.0) ) * delta
    end do
    integrate = total
  end function integrate
end module my_mod

! Main Program
program main
  use my_mod
  implicit none
  real :: value
  real, external :: fx_1, fx_2  ! external here is necessary
  value = integrate(fx_1, 1., 2., 100)
  print*, value
  value = integrate(fx_2, 1., 2., 100)
  print*, value
end program main

! --- Function 1
function fx_1(x)
  implicit none
  real :: x, fx_1
  fx_1 = x**2
end function fx_1

! --- Function 2
function fx_2(x)
  implicit none
  real :: x, fx_2
  fx_2 = x**3 + x**2
end function fx_2