def calc_sc_carter(slr, ecc, x):
    """
    Compute carter constant for the SC case (a = 0).

    Parameters:
        slr (float): semi-latus rectum [6, inf)
        ecc (float): eccentricity [0, 1)
        x (float): inclination value given by cos(theta_inc) (0, 1]
                   negative x -> retrograde
                   positive x -> prograde
    
    Returns:
        Q (float): Carter constant
    """
    ecc2 = ecc * ecc
    slr2 = slr * slr
    x2 = x * x

    Q = (slr2 * (-1 + x2)) / (3 + ecc2 - slr)
    return Q