We use the James Clerk Maxwell Telescope's SCUBA-2 camera to image a 400 arcmin^2 area surrounding the GOODS-N field. The 850 micron rms noise ranges from a value of 0.49 mJy in the central region to 3.5 mJy at the outside edge. From these data, we construct an 850 micron source catalog to 2 mJy containing 49 sources detected above the 4-sigma level. We use an ultradeep (11.5 uJy at 5-sigma) 1.4 GHz image obtained with the Karl G. Jansky Very Large Array together with observations made with the Submillimeter Array to identify counterparts to the submillimeter galaxies. For most cases of multiple radio counterparts, we can identify the correct counterpart from new and existing Submillimeter Array data. We have spectroscopic redshifts for 62% of the radio sources in the 9 arcmin radius highest sensitivity region (556/894) and 67% of the radio sources in the GOODS-N region (367/543). We supplement these with a modest number of additional photometric redshifts in the GOODS-N region (30). We measure millimetric redshifts from the radio to submillimeter flux ratios for the unidentified submillimeter sample, assuming an Arp 220 spectral energy distribution. We find a radio flux dependent K-z relation for the radio sources, which we use to estimate redshifts for the remaining radio sources. We determine the star formation rates (SFRs) of the submillimeter sources based on their radio powers and their submillimeter and find that they agree well. The radio data are deep enough to detect star-forming galaxies with SFRs >2000 solar masses per year to z~6. We find galaxies with SFRs up to ~6,000 solar masses per year over the redshift range z=1.5-6, but we see evidence for a turn-down in the SFR distribution function above 2000 solar masses per year. ; Comment: 23 pages, forgot to note that it is in press at The Astrophysical Journal