Explore recent advancements in the computation of Goncharov regulator integrals for K_4 classes on modular curves in this illuminating lecture. Delve into the collaborative work of Wadim Zudilin and François Brunault, which explicitly expresses these integrals using multiple modular values. Discover how these complex mathematical structures can be reduced to single L-values of modular forms, providing a significant simplification in the field. Over the course of 68 minutes, gain insights into the intricate connections between modular regulators, multiple modular values, and their applications in number theory and algebraic geometry.