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Strong gravitational lensing (SL) by galaxy clusters is a powerful probe of their inner mass distribution and a key test bed for cosmological models. However, the detection of SL events in wide-field surveys such as Euclid requires robust automated methods capable of handling the immense data volume generated. In this work, we present an advanced deep learning (DL) framework based on mask region-based convolutional neural networks (Mask R-CNNs) designed to autonomously detect and segment bright strongly lensed arcs in Euclid's multi-band imaging of galaxy clusters. The model was trained on a realistic simulated dataset of cluster-scale SL events constructed by injecting mock background sources into Euclidised Space Telescope images of ten massive lensing clusters, exploiting their high-precision mass models constructed with extensive spectroscopic data. The network was trained and validated on over 4500 simulated images and tested on an independent set of 500 simulations as well as on as real Euclid Quick Data Release (Q1) observations. The trained network achieves a high performance in identifying gravitational arcs in the test set, with a precision and recall of 76% and 58%, respectively, processing 2' , is open source and is available at . Hubble 2' images in a fraction of a second. When applied to a sample of visually confirmed Euclid Q1 cluster-scale lenses, our model recovers ≈ 66% of the gravitational arcs above the area threshold used during training. While the model shows promising results, limitations include the production of some false positives and challenges in detecting smaller, fainter arcs. Our results demonstrate the potential of advanced DL computer vision techniques for efficient and scalable arc detection in the effort towards enabling automated analysis of SL systems in current and future wide-field surveys. The code, ARTEMIDE https://github.com/LBasz/ARTEMIDE