It looks like you have a mathematical expression involving contour integration. Without an explicit question, a CAPTCHA does not usually come with a numeric solution, and it's not directly related to the problem described in Python (about counting computers in a server room).
Could you please provide the exact math question you're referring to? This will help in giving a detailed, step-by-step solution. If the question is indeed related to the counting of computers, please clarify that as well.