Crowd counting considers one of the most significant and challenging issues in computer vision and deep learning communities, whose applications are being utilized for various tasks. While this issue is well studied, it remains an open challenge to manage perspective distortions and scale variations. How well these problems are resolved has a huge impact on predicting a high-quality crowd density map. In this study, a hybrid and modified deep neural network (U-ASD Net), based on U-Net and adaptive scenario discovery (ASD), is proposed to get precise and effective crowd counting. The U part is produced by replacing the nearest upsampling in the encoder of U-Net with max-unpooling. This modification provides a better crowd counting performance by capturing more spatial information. The max-unpooling layers upsample the feature maps based on the max locations held from the downsampling process. The ASD part is constructed with three light pathways, two of which have been learned to reflect various densities of the crowd and define the appropriate geometric configuration employing various sizes of the receptive field. The third pathway is an adaptation path, which implicitly discovers and models complex scenarios to recalibrate pathway-wise responses adaptively. ASD has no additional branches to avoid increasing the complexity. The designed model is end-to-end trainable. This integration provides an effective model to count crowds in both dense and sparse datasets. It also predicts an elevated quality density map with a high structural similarity index and a high peak signal-to-noise ratio. Several comprehensive experiments on four popular datasets for crowd counting have been carried out to demonstrate the proposed method's promising performance compared to other state-of-the-art approaches. The proposed model achieves the lowest count error in terms of the MAE in ShanghaiTech Part A, Part B, and Mall datasets with 64.6, 7.5, and 1.8, respectively. Moreover, it achieves the lowest count error in terms of the MSE in ShanghaiTech Part B, UCF CC 50, UCSD, and Mall datasets with 12.4, 217.8, 2.1, 2.2, respectively. In addition, the proposed model accomplishes the best quality density maps on all the utilized datasets. Furthermore, a new dataset with its manual annotations, called Haramain with three different scenes and different densities, is introduced and used for evaluating the U-ASD Net.