fortran - confused about the intent of a function passed to a subroutine -

in doing following integral don't understand shouldn't intent of a,b in intent of f? shouldn't argument variables in subroutine have intent? confusing me though works know how?

also, see x intent (in) since y gets passed formal argument of f in subroutine. i'm not sure going on intents of subroutine seems integral should intent(out) right?

    program main     implicit none     real*10 :: integral     a= 1; b =2;n=1000;     call simpson(f,a,b,integral,n)      real*10 function f(x)                 real*10, intent(in) ::  x        f = x**(2.*charge)*exp(-a*x**2 -(b/2)*x**4)              end function f       subroutine simpson(f,a,b,integral,n)             real*10           :: integral, a, b      real*10           :: f      real*10 h, y ,s                                       integer n,     ! if n odd add +1 make     if((n/2)*2.ne.n) n=n+1     ! loop on n (number of intervals)     s = 0.0     h = (b-a)/dfloat(n)     i=2, n-2, 2         y   = a+dfloat(i)*h     s = s + 2.0*f(y) + 4.0*f(y+h)     end     integral = (s + f(a) + f(b) + 4.0*f(a+h))*h/3.0      end subroutine simpson         end program main 

if not defined, fortran compilers recognize variables having intent of inout.

procedure arguments, such f, different , not in, out, or inout. if specify f either of those, error message says along lines of

  error: procedure attribute conflicts intent attribute in 'f' @ (1)