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Speaker verification (SV) has recently attracted considerable research interest due to the growing popularity of virtual assistants. At the same time, there is an increasing requirement for an SV system: it should be robust to short speech segments, especially in noisy and reverberant environments. In this paper, we consider one more important requirement for practical applications: the system should be robust to an audio stream containing long non-speech segments, where a voice activity detection (VAD) is not applied. To meet these two requirements, we introduce feature pyramid module (FPM)-based multi-scale aggregation (MSA) and self-adaptive soft VAD (SAS-VAD). We present the FPM-based MSA to deal with short speech segments in noisy and reverberant environments. Also, we use the SAS-VAD to increase the robustness to long non-speech segments. To further improve the robustness to acoustic distortions (i.e., noise and reverberation), we apply a masking-based speech enhancement (SE) method. We combine SV, VAD, and SE models in a unified deep learning framework and jointly train the entire network in an end-to-end manner. To the best of our knowledge, this is the first work combining these three models in a deep learning framework. We conduct experiments on Korean indoor (KID) and VoxCeleb datasets, which are corrupted by noise and reverberation. The results show that the proposed method is effective for SV in the challenging conditions and performs better than the baseline i-vector and deep speaker embedding systems.