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The Age and The Mass of The αHerculis Triple-Star System From A MESA Grid of rotating stars with 1.3 <= M/Msun <= 8.0

α^1 Her is the second closest Asymptotic Giant Branch (AGB) star to the Sun, and the variable luminous M5 Ib-II member of a triple stellar system containing G8 III and A9 IV-V components. However, the mass of this important star was previously uncertain with published values ranging from ~2 - 15 Msun. As shown by this study, its fortuitous membership in a nearby resolved triple star system, makes it possible to determine its fundamental properties including its mass and age. We present over twenty years of VRI photometry of α^1 Her as well as Wing intermediate-band near-IR TiO and NIR continuum photometry. We introduce a new photometry-based calibration technique, and extract the effective temperature and luminosity of α^1 Her, in agreement with recent interferometric measures. We find, Teff=3280 +/- 87 K and log(L/Lsun)=3.92 +/- 0.14. With the MESA code, we calculate a dense grid of evolutionary tracks for Galactic low- to intermediate-mass (1.3 to 8 Msun) rotating stars from the pre-main sequence phase to the advanced AGB phase. We include atomic diffusion and rotation mechanisms to treat the effects of extra elemental mixing. Based on the observed properties of the αHerculis stars, we constrain the age of the system to lie in the range 0.41 to 1.25 Gyr. Thus, the mass of α^1 Her lies in the range 2.175 <= M/Msun <= 3.250. We compare our model-based age inference with recent tracks of the Geneva and STAREVOL codes, and show their agreement. In the prescribed mass range for α^1 Her, the observed 12C/13C and 16O/17O ratios are consistent (within 2σ) with the ratios predicted by the MESA, Geneva and STAREVOL codes.