The advancement of large language models (LLMs) has extended their use to dynamic and interactive real-world applications, where models engage continuously with their environment and potentially enhance their performance over time. Most existing LLM benchmarks evaluate LLMs on i.i.d. tasks, overlooking their ability to learn iteratively from past experiences. Our paper bridges this evaluation gap by proposing a novel framework, LLM-Evolve, which extends established benchmarks to sequential problem-solving settings. LLM-Evolve evaluates LLMs over multiple rounds, providing feedback after each round to build a demonstration memory that the models can query in future tasks. We applied LLM-Evolve to the MMLU, GSM8K, and AgentBench benchmarks, testing 8 state-of-the-art open-source and closed-source models. Results show that LLMs can achieve performance improvements of up to 17% by learning from past interactions, with the quality of retrieval algorithms and feedback significantly influencing this capability. These insights advocate for more understanding and benchmarks for LLMs’ performance in evolving interactive scenarios.