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

��^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 ��^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 ��^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 ��Herculis stars, we constrain the age of the system to lie in the range 0.41 to 1.25 Gyr. Thus, the mass of ��^1 Her lies in the range 2.175
Accepted to the Astronomical Journal. For the evolutionary tracks or the light curves, contact the corresponding author. 15 pages, 11 Figures and 6 Tables