Accurate vehicle trajectory prediction is critical for safe and efficient autonomous driving, especially in mixed traffic environments with both human-driven and autonomous vehicles. However, uncertainties introduced by inherent driving behaviors -- such as acceleration, deceleration, and left and right maneuvers -- pose significant challenges for reliable trajectory prediction. We introduce a Maneuver-Intention-Aware Transformer (MIAT) architecture, which integrates a maneuver intention awareness mechanism with spatiotemporal interaction modeling to enhance long-horizon trajectory predictions. We systematically investigate the impact of varying awareness of maneuver intention on both short- and long-horizon trajectory predictions. Evaluated on the real-world NGSIM dataset and benchmarked against various transformer- and LSTM-based methods, our approach achieves an improvement of up to 4.7% in short-horizon predictions and a 1.6% in long-horizon predictions compared to other intention-aware benchmark methods. Moreover, by leveraging an intention awareness control mechanism, MIAT realizes an 11.1% performance boost in long-horizon predictions, with a modest drop in short-horizon performance.