ATLAS measurements of the production of muons from heavy-flavor decays in root s(NN) = 2.76 TeV Pb+Pb collisions and root s = 2.76 TeV pp collisions at the LHC are presented. Integrated luminosities of 0.14 nb(-1) and 570 nb(-1) are used for the Pb+Pb and pp measurements, respectively, which are performed over the muon transverse momentum range 4 < pT < 14 GeV and for five Pb+Pb centrality intervals. Backgrounds arising from in-flight pion and kaon decays, hadronic showers, and misreconstructed muons are statistically removed using a template-fitting procedure. The heavy-flavor muon differential cross sections and per-event yields are measured in pp and Pb+Pb collisions, respectively. The nuclear modification factor R-AA obtained from these is observed to be independent of pT, within uncertainties, and to be less than unity, which indicates suppressed production of heavy-flavor muons in Pb+Pb collisions. For the 10% most central Pb+Pb events, the measured R-AA is approximately 0.35. The azimuthal modulation of the heavy-flavor muon yields is also measured and the associated Fourier coefficients v(n) for n = 2, 3, and 4 are given as a function of pT and centrality. They vary slowly with pT and show a systematic variation with centrality which is characteristic of other anisotropy measurements, such as that observed for inclusive hadrons. The measured R-AA and v(n) values are also compared with theoretical calculations.