This paper presents the Never Ending Open Learning Adaptive Framework (NEOLAF), an integrated neural-symbolic cognitive architecture that models and constructs intelligent agents. The NEOLAF framework is a superior approach to constructing intelligent agents than both the pure connectionist and pure symbolic approaches due to its explainability, incremental learning, efficiency, collaborative and distributed learning, human-in-the-loop enablement, and self-improvement. The paper further presents a compelling experiment where a NEOLAF agent, built as a problem-solving agent, is fed with complex math problems from the open-source MATH dataset. The results demonstrate NEOLAF's superior learning capability and its potential to revolutionize the field of cognitive architectures and self-improving adaptive instructional systems.