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The first Pop III stars formed out of primordial, metal free gas, in minihalos at z>20, and kickstarted the cosmic processes of reionizaton and enrichment. While these stars are likely more massive than their enriched counterparts, the current unknowns of their astrophysics include; when the first Pop III stars ignited, how massive they were, and when and how the era of the first stars ended. Investigating these questions requires an exploration of a multi-dimensional parameter space, including the slope of the Pop III stellar initial mass function (IMF) and the strength of the non-ionizing UV background. In this work, we present a novel model which treats both the slope and maximum mass of Pop III stars as truly free parameters while including the physics of the fragmentation of primordial gas. Our results also hint at a non-universal Pop III IMF which is dependent on the efficiency of primordial gas fragmentation. Our relatively simple model reproduces the results from hydrodynamic simulations, but with a computational efficiency which allows us to investigate the observable differences between a wide range of potential Pop III IMFs. In addition, the evolution of the number density of Pop III stars may provide insight into the evolution of the H2 dissociating background. While the slope of the Pop III IMF does not significantly affect the predicted number density of the first stars, more top heavy IMFs produce Pop III star clusters which are 2-3 magnitudes brighter than their more bottom heavy counterparts. While the Pop III star clusters are too dim for direct detection by JWST, we find they are within the reach of gravitational lensing.