Previous studies in robotic-assisted surgery (RAS) have studied cognitive workload by modulating surgical task difficulty, and many of these studies have relied on self-reported workload measurements. However, contributors to and their effects on cognitive workload are complex and may not be sufficiently summarized by changes in task difficulty alone. This study aims to understand how multi-task requirement contributes to the prediction of cognitive load in RAS under different task difficulties. Multimodal physiological signals (EEG, eye-tracking, HRV) were collected as university students performed simulated RAS tasks consisting of two types of surgical task difficulty under three different multi-task requirement levels. EEG spectral analysis was sensitive enough to distinguish the degree of cognitive workload under both surgical conditions (surgical task difficulty/multi-task requirement). In addition, eye-tracking measurements showed differences under both conditions, but significant differences of HRV were observed in only multi-task requirement conditions. Multimodal-based neural network models have achieved up to 79% accuracy for both surgical conditions.