real function integral(a, h, m)
! real function integral(a, h, m)
! performs midpoint integration with forloop
implicit none
real :: a, h, x
integer :: m, i
integral = 0.0        ! initialize integral
do i=1,m
   x = a+(i-0.5)*h    ! mid-point of increment i
   integral = integral + cos(x)*h 
enddo
return
end