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We use the first release of the SDSS/MaStar stellar library comprising ∼9000, high S/N spectra, to calculate integrated spectra of stellar population models. The models extend over the wavelength range 0.36-1.03 μm and share the same spectral resolution (R~1800) and flux calibration as the SDSS-IV/MaNGA galaxy data. The parameter space covered by the stellar spectra collected thus far allows the calculation of models with ages and chemical composition in the range t>200 Myr, -2 < [Z/H] < + 0.35, which will be extended as MaStar proceeds. Notably, the models include spectra for dwarf Main Sequence stars close to the core H-burning limit, as well spectra for cold, metal-rich giants. Both stellar types are crucial for modelling λ >0.7μm absorption spectra. Moreover, a better parameter coverage at low metallicity allows the calculation of models as young as 500 Myr and the full account of the Blue Horizontal Branch phase of old populations. We present models adopting two independent sets of stellar parameters (Teff, logg, [Z/H]). In a novel approach, their reliability is tested ’on the fly’ using the stellar population models themselves. We perform tests with Milky Way and Magellanic Clouds globular clusters, finding that the new models recover their ages and metallicities remarkably well, with systematics as low as a few per cent for homogeneous calibration sets. We also fit a MaNGA galaxy spectrum, finding residuals of the order of a few per cent comparable to the state-of-art models, but now over a wider wavelength range.