def METHOD_NAME(R, r):
    """
    Compute the surface area of the intersection of sphere of radius R centered
    at (0, 0, 0) with a ball of radius r centered at (R, 0, 0).
    Parameters
    ----------
    R : float, sphere radius
    r : float, ball radius
    Returns
    --------
    area: float, the surface are.
    """
    x = (2 * R**2 - r**2) / (2 * R)  # x coord of plane
    if x >= -R:
        return 2 * np.pi * R * (R - x)
    if x < -R:
        return 4 * np.pi * R**2