Build a fake desktop OS with working apps

Build a single self-contained HTML file that simulates a small fake desktop operating system in the browser. Requirements: a desktop with a wallpaper, a taskbar/dock, and clickable app icons; draggable, closable windows (open multiple at once, bring-to-front on click); and at least THREE genuinely working built-in apps: (1) a Calculator that performs correct arithmetic, (2) a Paint app with a freehand brush, an eraser, and color/brush-size controls drawing onto a canvas, and (3) a Notes app where you can create, edit, and delete notes. Each app opens in its own window. Everything must actually function — the calculator must compute correctly, the brush must draw, the notes must persist while the page is open. Design it with real polish: cohesive theme, good spacing and alignment, smooth interactions. All CSS in a `<style>` tag and all JS in a `<script>` tag — no external libraries, images, or fonts. Return ONLY a single complete self-contained HTML file, no markdown fences, no explanation.