We present a measurement of the cosmic microwave background ( CMB ) temperature power spectrum using data from the recently completed South Pole Telescope Sunyaev-Zel ’ dovich ( SPT-SZ ) survey . This measurement is made from observations of 2540 deg ^ { 2 } of sky with arcminute resolution at 150 GHz , and improves upon previous measurements using the SPT by tripling the sky area . We report CMB temperature anisotropy power over the multipole range 650 < \ell < 3000 . We fit the SPT bandpowers , combined with the seven-year Wilkinson Microwave Anisotropy Probe ( WMAP 7 ) data , with a six-parameter \Lambda CDM cosmological model and find that the two datasets are consistent and well fit by the model . Adding SPT measurements significantly improves \Lambda CDM parameter constraints ; in particular , the constraint on \theta _ { s } tightens by a factor of 2.7 . The impact of gravitational lensing is detected at 8.1 \sigma , the most significant detection to date . This sensitivity of the SPT+ WMAP 7 data to lensing by large-scale structure at low redshifts allows us to constrain the mean curvature of the observable universe with CMB data alone to be \mbox { $ \Omega _ { k } $ } = -0.003 ^ { +0.014 } _ { -0.018 } . Using the SPT+ WMAP 7 data , we measure the spectral index of scalar fluctuations to be n _ { s } = 0.9623 \pm 0.0097 in the \Lambda CDM model , a 3.9 \sigma preference for a scale-dependent spectrum with n _ { s } < 1 . The SPT measurement of the CMB damping tail helps break the degeneracy that exists between the tensor-to-scalar ratio r and n _ { s } in large-scale CMB measurements , leading to an upper limit of r < 0.18 ( 95 % C.L . ) in the \Lambda CDM+ r model . Adding low-redshift measurements of the Hubble constant ( H _ { 0 } ) and the baryon acoustic oscillation ( BAO ) feature to the SPT+ WMAP 7 data leads to further improvements . The combination of SPT+ WMAP 7+ H _ { 0 } +BAO constrains n _ { s } = 0.9538 \pm 0.0081 in the \Lambda CDM model , a 5.7 \sigma detection of n _ { s } < 1 , and places an upper limit of r < 0.11 ( 95 % C.L . ) in the \Lambda CDM+ r model . These new constraints on n _ { s } and r have significant implications for our understanding of inflation , which we discuss in the context of selected single-field inflation models .