We report the results of a direct imaging survey of A- and F-type main sequence stars searching for giant planets. A/F stars are often the targets of surveys, as they are thought to have more massive giant planets relative to solar-type stars. However, most imaging is only sensitive to orbital separations $>$30 AU, where it has been demonstrated that giant planets are rare. In this survey, we take advantage of the high-contrast capabilities of the Apodizing Phase Plate coronagraph on NACO at the Very Large Telescope. Combined with optimized principal component analysis post-processing, we are sensitive to planetary-mass companions (2 to 12 $M_{rm Jup}$) at Solar System scales ($leq$30 AU). We obtained data on 13 stars in L-band and detected one new companion as part of this survey: an M$6.0pm0.5$ dwarf companion around HD 984. We re-detect low-mass companions around HD 12894 and HD 20385, both reported shortly after the completion of this survey. We use Monte Carlo simulations to determine new constraints on the low-mass ($<$80 $M_{rm Jup}$) companion frequency, as a function of mass and separation. Assuming solar-type planet mass and separation distributions, normalized to the planet frequency appropriate for A-stars, and the observed companion mass-ratio distribution for stellar companions extrapolated to planetary masses, we derive a truncation radius for the planetary mass companion surface density of $<$135 AU at 95% confidence.
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