  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 micron 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 as spectra for cold, metal-rich
giants. Both stellar types are crucial for modelling lambda>0.7 micron
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 (T_eff, 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.
