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The Planck and Herschel missions are currently measuring the far-infrared to millimeter emission of dust, which combined with existing IR data, will for the first time provide the full spectral energy distribution (SED) of the galactic interstellar medium dust emission, from the mid-IR to the mm range, with an unprecedented sensitivity and down to spatial scales ~30″. Such a global SED will allow a systematic study of the dust evolution processes (e.g. grain growth or fragmentation) that directly affect the SED because they redistribute the dust mass among the observed grain sizes. The dust SED is also affected by variations of the radiation field intensity. Here we present a versatile numerical tool, DustEM, that predicts the emission and extinction of dust grains given their size distribution and their optical and thermal properties. In order to model dust evolution, DustEM has been designed to deal with a variety of grain …