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Evaluation of multi-loop multi-scale Feynman integrals is currently a key bottleneck to obtaining high-precision theoretical predictions for collider phenomenology. In this talk, I will discuss recent progress in analytically evaluating Feynman integrals using their Mellin-Barnes representation by employing the geometry of conic hulls and triangulations. I will further discuss its connection to the geometry of expansion by regions and how to obtain high-precision numerical results by combining it with the differential equation approach.