Breast cancer is detected in one out of eight females worldwide. Principally biomedical image processing techniques work with images captured by a microscope and then analyzed with the help of different algorithms and methods. Instead of microscopic image diagnosis, machine learning algorithms are now incorporated to detect and diagnose therapeutic imagery. Computeraided mechanisms are used for better efficiency and reliability compared with manual pathological detection systems. Machine learning algorithms detect tumors by extracting features through a convolutional neural network (CNN) and then classifying them using a fully connected network. As Machine learning does not require prior expertise, it is profoundly used in biomedical imaging. This article has customized a convolutional neural network by mathematical modeling of a proposed activation function. We have obtained an appreciable prediction accuracy of up to 99%, along with a precision of 0.97.