from numbers import Number

def clamp(low: Number, high: Number, num: Number) -> Number:
    """Limit range of ``num`` between ``low`` and ``high``"""
    return max(low, min(high, num))

def circrect(a: Number, b: tuple[Number, Number], c: tuple[Number, Number]) -> Number:
    """
    Calculate the area of the overlap between a circle with radius ``a`` and a
    rectangle defined by opposing corner points ``b`` and ``c``.

    Args:
        a: circle radius
        b: first corner coordinate of rectangle
        c: second corner coordinate of rectangle (opposite of b)

    Returns:
        Overlap area (square units)
    """

    # normalize input variables
    a = abs(a)
    b, c = (
      (min(b[0], c[0]), min(b[1], c[1])),
      (max(b[0], c[0]), max(b[1], c[1])),
    )
    b = (clamp(-a, a, b[0]), clamp(-a, a, b[1]))
    c = (clamp(-a, a, c[0]), clamp(-a, a, c[1]))

    return 0

if __name__ == "__main__":
    print(
        circrect(1, (-1, -1), (1, 1)), # pi
        circrect(1, (1, 1), (-1, -1)), # pi
        circrect(-1, (-1, -1), (1, 1)), # pi
        circrect(2, (10, 10), (11, 11)), # 0
        circrect(10, (0, 0), (1, 1)), # 1
    )