In research areas such as mobile robotics and computer vision, energy and computational efficiency have become critical. This has greatly increased interest in high-efficiency neuromorphic hardware and spiking neural networks. Because neuromorphic hardware is not yet widely available, spiking neural network studies are conducted by simulations. There are numerous simulators available today, each designed for a specific purpose. In this paper, a novel and open- source package (SPAYK) for simulating spiking neural networks is presented. SPAYK has been proposed to speed up spiking neural network research. In the majority of simulators, networks are expressed with differential equations and require advanced neuroscience knowledge since such simulators are generally designed for brain and neuroscience research. SPAYK, on the other hand, is specifically designed as a framework to easily design spiking neural networks for practical problems. SPAYK is an easy-to-use Python package. There are three fundamental classes in the core: the model class for creating neuron groups, the organization class for simulating tissues, and the learning class for synaptic plasticity. While developing and testing the SPAYK environment, various experiments were carried out. This study includes three of these experiments. In the first experiment, we investigated the behavior of a group of Izhikevich neurons for visual stimuli. Also, a single Izhikevich neuron has been trained to respond to a particular label in a supervised manner with synaptic plasticity. In the second experiment, a well-known experiment was repeated to validate SPAYK. In this experiment, a neuron trained by synaptic plasticity can recognize repetitive patterns in a spike train. In the third experiment, a similar neuron was simulated with stimuli with multiple labels adapted from the MNIST dataset. It has been shown that the neuron can classify a particular label by synaptic plasticity. All these experiments and the SPAYK environment are presented as open-source tools.