Program_Module

module integration_library
  implicit none
  contains
  function calculatex (x)
    double precision :: calculatex
    double precision, intent (in) :: x
    calculatex = x **4 * log(x + (x**2 + 1)**0.5 )
  end function

  function area (y1,y2,dx)
    double precision :: area
    double precision, intent (in) :: y1,y2,dx
    area = ((y1 + y2) * dx) / 2.0
  end function
end module integration_library

program integration
  use integration_library, only:calculatex,area
  implicit none
  double precision :: a,b,r,y1,y2,dx
  integer :: i,n
  10 format(a,1x,f20.10)
  
  read (*,*) a
  read (*,*) b
  read (*,*) n
  
  dx = (b-a) / n
  r = 0
  do i=1,n
    y1 = calculatex (a + ((i-1) * dx))
    y2 = calculatex (a + (i * dx))
    r = r + area(y1,y2,dx)
  end do
  write(*,10) 'area =', r
end program