Life On VM

import math

def calculate_segment(R,x1,y1,x2,y2):
    ang1 = math.atan(y1/x1)
    ang2 = math.atan(y2/x2)
    ang = math.fabs(ang1 - ang2)
    area = (ang/math.pi/2)*math.pi*R**2
    cord = math.sqrt((x1-x2)**2 + (y1-y2)**2)
    pie = math.cos(ang/2)*R*cord/2
    return area - pie

if __name__ == '__main__':
    #in_filename = "C-small-practice.in"
    #in_filename = "C-dummy.in"
    in_filename = "C-large-practice.in"
    #out_filename = "C-small.out"
    out_filename = "C-large.out"
    
    in_file = open(in_filename, 'r')
    num_cases = int(in_file.readline())
    out_file = open(out_filename, 'w')

    for c in range(0,num_cases):
        f, R, t, r, g = [float(x) for x in in_file.readline().split(' ')]
        r = r + f
        g = g - 2*f
        t = t + f
        x1 = r
        y1 = r
        
        # Is the interested point inside the circle
        is_inside = lambda x,y : (x**2 + y**2) <= (R-t)**2
        
        # Get y from x, or get x from y
        get_pair = lambda x : math.sqrt((R-t)**2 - x**2)

        if g > 0.0:
            area = 0.0
            while x1 <= R-t:
                while y1 <= R-t:
                    x2 = x1 + g
                    y2 = y1 + g
                    if is_inside(x1,y1):
                        if is_inside(x2,y2):
                            # Full rectangle is inside
                            area = area + (x2-x1)*(y2-y1)
                        else:
                            x1_y2_in = is_inside(x1,y2)
                            x2_y1_in = is_inside(x2,y1)
                            if x1_y2_in and x2_y1_in:
                                xt = get_pair(y2)
                                yt = get_pair(x2)
                                area = area + (x2-x1)*(y2-y1)
                                area = area - (x2-xt)*(y2-yt)/2
                                area = area + calculate_segment(R-t,xt,y2,x2,yt)
                            elif x1_y2_in and not x2_y1_in:
                                xt2 = get_pair(y2)
                                xt1 = get_pair(y1)
                                area = area + (xt2 + xt1 - 2*x1)*(y2-y1)/2
                                area = area + calculate_segment(R-t,xt2,y2,xt1,y1)
                            elif not x1_y2_in and x2_y1_in:
                                yt1 = get_pair(x1)
                                yt2 = get_pair(x2)
                                area = area + (yt1 + yt2 - 2*y1)*(x2-x1)/2
                                area = area + calculate_segment(R-t,x1,yt1,x2,yt2)
                            else:
                                yt = get_pair(x1)
                                xt = get_pair(y1)
                                area = area + (yt-y1)*(xt-x1)/2
                                area = area + calculate_segment(R-t,x1,yt,xt,y1)
                    y1 = y1 + g + 2*r
                x1 = x1 + g + 2*r
                y1 = r
            all_area = math.pi*R*R/4
            prob = (all_area - area)/all_area
        else:
            prob = 1.0
        out_file.write("Case #%d: %f\n" % (c+1, prob))

    out_file.close()