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We present a new annotated microscopic cellular image dataset to improve the effectiveness of machine learning methods for cellular image analysis. Cell counting is an important step in cell analysis. Typically, domain experts manually count cells in a microscopic image. Automated cell counting can potentially eliminate this tedious, time-consuming process. However, a good, labeled dataset is required for training an accurate machine learning model. Our dataset includes microscopic images of cells, and for each image, the cell count and the location of individual cells. The data were collected as part of an ongoing study investigating the potential of electrical stimulation to modulate stem cell differentiation and possible applications for neural repair. Compared to existing publicly available datasets, our dataset has more images of cells stained with more variety of antibodies (protein components of immune responses against invaders) typically used for cell analysis. The experimental results on this dataset indicate that none of the five existing models under this study are able to achieve sufficiently accurate count to replace the manual methods. The dataset is available at https://figshare.com/articles/dataset/Dataset/21970604.