33 pages, 8 figures.We study compactifications of type IIA string theory on Calabi-Yau manifolds that are mirror to a subset of the type IIB LARGE-volume models. A combination of flux, alpha' corrections and non-perturbative effects stabilises the moduli in a non-supersymmetric AdS vacuum. This vacuum has the feature that the (ten-dimensional) string coupling is exponentially small which can naturally lead to a TeV supersymmetry breaking scale with an intermediate string scale. The AdS vacuum can be uplifted to a dS one through the introduction of D6 branes, and complex-structure modular inflation can be realised.EP is supported by a STFC Postdoctoral Fellowship. GT is supported by MEC and FEDER under grant FPA2006-05485, by CAM under grant HEPHACOS P-ESP-00346, and by the UniverseNet network (MRTN-CT-2006-035863).Peer reviewed