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We carried out light curve solutions of four detached binaries observed by Kepler. As a result, their orbital inclinations, temperatures and relative stellar radii were determined. KIC 10031409 and KIC 11228612 reveal partial eclipses while the components of KIC 11403216 and KIC 11913071 undergo total eclipses. The secondary component of KIC 11403216 is probably a very late M dwarf or brown dwarf. The out-of-eclipse brightness of KIC 10031409, KIC 11228612 and KIC 11913071 vary with the orbital period and might be explained by spots on synchronously-rotating star(s). The out-of-eclipse variability of KIC 11403216 is with a period that is a third of its orbital period and may be due to spot on asynchronous rotating component. The resonance 1:3 needs future study of KIC 11403216.

We carried out light curve solutions of the Kepler light curves of twenty detached eclipsing binaries with circular orbits and determined the orbital inclinations, temperatures. relative radii and luminosities of their components. We studied the quality of the solutions with respect to the adopted limb-darkening law and its coefficients. The detailed tracing of the numerous and uninterrupted data of our targets gave us an unique possibility to detect and learn their spot and flare activity. We established that the out-of-eclipse variability of the most targets gradually changes from small-amplitude two-waved type to big-amplitude one-waved type and vice versa, i.e. their spot activity cycles pass through phase of two almost diametrically opposite spots and phase of big polar cool spot. We found that the low-temperature targets show flare activity of UV Cet-type with amplitudes of 0.002-0.22 mag and duration of up to several hours. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]