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The study of the quiet Sun in gamma rays started over a decade ago, andrapidly gained a wide interest. Gamma rays from the quiet Sun are produced byCosmic Rays (CRs) interacting with its surface (disk component) and with itsphoton field (spatially extended inverse-Compton component, IC). The lattercomponent is maximum close to the Sun and it is above the background even atlarge angular distances, extending over the whole sky. First detected withEGRET, it is studied now with Fermi-LAT with high statistical significance.  Observations of the IC component allow us to obtain information on CRelectrons and positrons close to the Sun and in the heliosphere for the variousperiods of solar activity and polarity. They allow to learn about CRinteractions and propagation close to stars, in the heliosphere and on thesolar surface, and to understand the Sun itself, its environment, and itsactivity. Analyses of solar observations are usually model-driven. Henceadvances in model calculations and constraints from precise CR measurements aretimely and needed.  Here we present our StellarICS code to compute the gamma-ray IC emission fromthe Sun and also from single stars. The code is publicly available and it isextensively used by the scientific community to analyze Fermi-LAT data. It hasbeen used by the Fermi-LAT collaboration to produce the solar models releasedwith the FSSC Fermi Tools. Our modeling provides the basis for analyzing andinterpreting high-energy data of the Sun and of stars.  After presenting examples of updated solar IC models in the Fermi-LAT energyrange that account for the various CR measurements, we extend the models tokeV, MeV, and TeV energies for predictions for future possible telescopes suchas AMEGO, GECCO, e-ASTROGAM, HAWC, LHAASO, SWGO, and present X-ray telescopes.We also present predictions for some of the closest and most luminous stars.

StellarICS: Inverse Compton Emission from the Quiet Sun and Stars from keV to TeV