  The extreme ultraviolet (EUV) spectra of distant star-forming regions cannot
be probed directly using either ground- or space-based telescopes due to the
high cross-section for interaction of EUV photons with the interstellar medium.
This makes EUV spectra poorly constrained. The mm/submm recombination lines of
H and He, which can be observed from the ground, can serve as a reliable probe
of the EUV. Here we present a study based on ALMA observations of three
Galactic ultra-compact HII regions and the starburst region Sgr B2(M), in which
we reconstruct the key parameters of the EUV spectra using mm recombination
lines of HI, HeI and HeII. We find that in all cases the EUV spectra between
13.6 and 54.4 eV have similar frequency dependence: L_{\nu}~ \nu^{-4.5 +/-
0.4}. We compare the inferred values of the EUV spectral slopes with the values
expected for a purely single stellar evolution model (Starburst99) and the
Binary Population and Spectral Synthesis code (BPASS). We find that the
observed spectral slope differs from the model predictions. This may imply that
the fraction of interacting binaries in HII regions is substantially lower than
assumed in BPASS. The technique demonstrated here allows one to deduce the EUV
spectra of star forming regions providing critical insight into photon
production rates at \lambda < 912 A and can serve as calibration to starburst
synthesis models, improving our understanding of star formation in distant
universe and the properties of ionizing flux during reionization.
