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We investigated a three-dimensional semi-infinite spin-1/2 system bounded by a spin-1 surface using a Monte Carlo simulation based on the Metropolis algorithm. The exchange interactions and crystal field effects on phase diagrams, magnetizations, and susceptibilities were investigated. The phase diagrams in three planes were presented due to the competition between specific system parameters. The system demonstrated ordinary, extraordinary, surface, and special second-order phase transitions, as well as a surface first-order phase transition. Furthermore, tricritical and critical end-points were discovered. [ABSTRACT FROM AUTHOR]