def vol_spheres_intersect(
    radius_1: float, radius_2: float, centers_distance: float
) -> float:
    if radius_1 < 0 or radius_2 < 0 or centers_distance < 0:
        raise ValueError("vol_spheres_intersect() only accepts non-negative values")
    if centers_distance == 0:
        return vol_sphere(min(radius_1, radius_2))

    h1 = (
        (radius_1 - radius_2 + centers_distance)
        * (radius_1 + radius_2 - centers_distance)
        / (2 * centers_distance)
    )
    h2 = (
        (radius_2 - radius_1 + centers_distance)
        * (radius_2 + radius_1 - centers_distance)
        / (2 * centers_distance)
    )

    return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)