Is it a Data Mining Task?

(i) Dividing customers according to profitability

Yes, this is a data mining task.
This is a clustering/segmentation problem — grouping customers into meaningful segments based on profitability-related attributes (purchase frequency, spend, margin) without predefined labels. Discovering these natural groupings from raw transaction/customer data is a core data mining functionality (unsupervised clustering).

(ii) Monitoring and predicting failures in a hydropower plant

Yes, this is a data mining task (specifically the "predicting" part).

• Monitoring alone (just observing sensor readings in real time) is not mining — it's plain data collection/surveillance.
• Predicting failures, however, requires learning patterns from historical sensor/operational data to forecast future failures — this is a classification/prediction task, a core data mining functionality.

So both qualify as data mining tasks, but for different reasons: (i) because segmentation without labels = clustering, and (ii) because predicting future failures from historical patterns = predictive modeling — not because "monitoring" itself is mining.