Data science (DS) programs, typically built on popular DS libraries (such as PyTorch and NumPy) with thousands of APIs, serve as the cornerstone for various mission-critical domains such as financial systems, autonomous driving software, and coding assistants. Recently, large language models (LLMs) have been widely applied to generate DS programs across diverse scenarios, such as assisting users for DS programming or detecting critical vulnerabilities in DS frameworks. Such applications have all operated under the assumption, that LLMs can implicitly model the numerical parameter constraints in DS library APIs and produce valid code. However, this assumption has not been rigorously studied in the literature. In this paper, we empirically investigate the proficiency of LLMs to handle these implicit numerical constraints when generating DS programs. We studied 28 widely used APIs from PyTorch and NumPy, and scrutinized the LLMs’ generation performance in different levels of granularity: full programs, all parameters, and individual parameters of a single API. We evaluated both state-of-the-art open-source and closed-source models. The results show that LLMs are great at generating simple DS programs, particularly those that follow common patterns seen in training data. However, as we increase the difficulty by providing more complex/unusual inputs, the performance of LLMs drops significantly. We also observe that GPT-4-Turbo can sustain much higher performance overall, but still cannot handle arithmetic API constraints well. In summary, while LLMs exhibit the ability to memorize common patterns of popular DS API usage through massive training, they overall lack genuine comprehension of the underlying numerical constraints.