I'm trying to write a function that calculates the surface area of a prolate or oblate spheroid. Here's a link to where I got the formulas (http://en.wikipedia.org/wiki/Prolate_spheroid & http://en.wikipedia.org/wiki/Oblate_spheroid). I think I've written them wrong, but here is my code so far;

from math import pi, sqrt, asin, degrees, tanh 

def checkio(height, width):
    height = float(height) 
    width = float(width) 
    lst = []
    if height == width:
        r = 0.5 * width
        surface_area = 4 * pi * r**2
        surface_area = round(surface_area, 2) 
        lst.append(surface_area)
    elif height > width: #If spheroid is prolate 
        a = 0.5 * width
        b = 0.5 * height
        e = 1 - a / b
        surface_area = 2 * pi * a**2 * (1 + b / a * e * degrees(asin**-1(e)))
        surface_area = round(surface_area, 2) 
        lst.append(surface_area) 
    elif height < width: #If spheroid is oblate 
        a = 0.5 * height
        b = 0.5 * width
        e = 1 - b / a
        surface_area = 2 * pi * a**2 * (1 + 1 - e**2 / e * tanh**-1(e)) 
        surface_area = round(surface_area, 2)
        lst.append(surface_area, 2)
    return lst