Can't input value in f(x) in this Fortran code?

Question

    program prob_1
    implicit real*8(a-h, o-z)
    f(x) = x**2-cos(x)
    df(x) = 2*x+sin(x)
    x0 = 0, x1 = 1
    do i = 1, 3
        if (f((x0+x1)/2) < 0)
            x0 = (x0+x1)/2
        else
            x1 = (x0+x1)/2
    end do
    print *,"x = ", x
end program

I'm just starting to use Fortran 90. Now I'm using Code::blocks but I don't know exactly which line the error exists on.

I guess the problem is f((x0+x1)/2) < 0 but don't know actually what is the real error. what's problem is here?

Answer 1

Be advised that statement functions, the function definitions the OP uses, are obsolescent.

B.3.4 Statement functions

1. Statement functions are subject to a number of non intuitive restrictions and are a potential source of error because their syntax is easily confused with that of an assignment statement.
2. The internal function is a more generalized form of the statement function and completely supersedes it.

_{source: F2018 Standard}

Also the notation REAL*8 or anything of that form has never been part of any Fortran standard (see here):

I would suggest to rewrite the code as:

program prob_1
    implicit none
    double precision :: x1,x0
    integer          :: i
    x0 = 0; x1 = 1
    do i = 1, 3
        if (f((x0+x1)/2.0D0) < 0) then
            x0 = (x0+x1)/2.0D0
        else
            x1 = (x0+x1)/2.0D0
        endif
    end do
    print *,"x = ", (x0+x1)/2.0D0
contains
    function f(x)
      double precision, intent(in) :: x
      double precision             :: f
      f = x**2-cos(x)
    end function f
   function df(x)
      double precision, intent(in) :: x
      double precision             :: df
      df = 2.0D0*x+sin(x)
    end function df
end program

Answer 2

If you change your program as follows then it will compile:

program prob_1
    implicit real*8(a-h, o-z)
    f(x) = x**2-cos(x)
    df(x) = 2*x+sin(x)
    x0 = 0; x1 = 1
    do i = 1, 3
        if (f((x0+x1)/2) < 0) then
            x0 = (x0+x1)/2
        else
            x1 = (x0+x1)/2
        endif
    end do
    print *,"x = ", x
end program

As mentionned in the comments, you have to add the semicolon ; to separate statements in one line and you have to add the then as well as endif to your if condition.

Hope it helps.