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```typescript
// AI Dev Tool: Next.js Expo Monorepo Boilerplate with Falstad Math Simulations
// Description: A production-ready Next.js Expo monorepo boilerplate with integrated Falstad math simulations.

import { createClient } from '@supabase/supabase-js';
import { NextApiRequest, NextApiResponse } from 'next';
import { FalstadSimulation } from 'falstad';

// Initialize Supabase client
const supabaseUrl = 'https://your-supabase-instance.supabase.co';
const supabaseKey = 'your-supabase-key';
const supabaseSecret = 'your-supabase-secret';
const supabase = createClient(supabaseUrl, supabaseKey, supabaseSecret);

// Define the API route for Falstad simulations
async function falstadSimulation(req: NextApiRequest, res: NextApiResponse) {
  try {
    // Get the simulation parameters from the request body
    const { simulationName, parameters } = req.body;

// Initialize the Falstad simulation
    const simulation = new FalstadSimulation(simulationName, parameters);

// Run the simulation and get the results
    const results = await simulation.run();

// Save the results to Supabase
    const { data, error } = await

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