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In this study, we use numerical simulations to investigate the flow field induced by a single magnetic microrobot rotating with a constant angular speed about an axis perpendicular to an underlying surface. A parallel solver for steady Stokes flow equations based on the boundary-element method is used for simulating these flows. A simple transformation is introduced to extend the predictive capability of the solver to cases with small unsteadiness. Flows induced by four simple robot shapes are investigated: sphere, upright cylinder, horizontally-laid cylinder, and five-pointed star-shaped prism. Shapes with cross-sections that are axisymmetric about the rotation axis (sphere and upright cylinder) generate time-invariant flow fields, which could be useful for applications such as micromanipulation. Non-axisymmetric shapes (horizontally-laid cylinder and the star-shaped prism) induce significant unsteadiness inside the flow field, which could be desirable for applications such as micromixing. Furthermore, a slender horizontally-laid cylinder generates substantially three-dimensional flows, an added benefit for micromixing applications. The presence of nearby walls such as a bottom substrate or sidewalls has a retarding effect on the induced flows, which is quantified. Finally, we present the driving torque and power-consumption of these microrobots rotating in viscous liquids. The numerical modeling platform used in this work can enable future optimal microrobot designs for a given application requirement.