The X-ray spectra of X-ray binaries are dominated by emission of either soft or hard X-rays which defines their soft and hard spectral states. Cygnus X-3 is amongst the list of X-ray binaries that show quite complex behavior, with various distinct spectral states. Because of its softness and intrinsic low flux above typically 50 keV, very little is known about the hard X/soft gamma-ray (100-1000 keV) emission in Cygnus X-3. Using the whole INTEGRAL data base, we aim to explore the 3-1000 keV spectra of Cygnus X-3. This allows to probe this region with the highest sensitivity ever, and search for the potential signature of a high-energy non-thermal component as sometimes seen in other sources. Our work is based on state classification carried out in previous studies with data from the Rossi X-Ray Timing Explorer. We extend this classification to the whole INTEGRAL data set and perform a long-term state-resolved spectral analysis. Six stacked spectra were obtained using 16 years of data from JEM-X, ISGRI, and SPI. We extract stacked images in three different energy bands, and detect the source up to 200 keV. In the hardest states, our phenomenological approach reveals the presence of an component > 50 keV in addition to the component usually interpreted as thermal Comptonization. We apply a more physical model of hybrid thermal/nonthermal corona to characterize this component and compare our results with those of previous studies. Our modeling indicates a more efficient acceleration of electrons in states where major ejections are observed. We find a dependence of the photon index of the power law as a function of the strong orbital modulation of the source in the Flaring InterMediate (FIM) state. This dependence could be due to a higher absorption when Cygnus X-3 is behind its companion. However, the uncertainties on the density column prevent us from drawing conclusions.
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