## Problem Description and Symbolic Representation

The problem can be broken down into the following components:

- **Variables:**
  - $x_1$ = Number of algebra questions
  - $x_2$ = Number of calculus questions

- **Objective Function:**
  - Maximize $1x_1 + 3x_2$ (Maximize the total score, with algebra questions worth 1 point each and calculus questions worth 3 points each)

- **Constraints:**
  - $x_1 + x_2 \leq 25$ (At most 25 questions in total)
  - $x_1 \geq 10$ (At least 10 algebra questions)
  - $x_2 \geq 6$ (At least 6 calculus questions)
  - $x_1 \leq 15$ (No more than 15 algebra questions)
  - $x_2 \leq 15$ (No more than 15 calculus questions)
  - $x_1, x_2 \geq 0$ and are integers (Only non-negative integers are valid)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'algebra questions'), ('x2', 'calculus questions')],
    'objective_function': '1*x1 + 3*x2',
    'constraints': [
        'x1 + x2 <= 25',
        'x1 >= 10',
        'x2 >= 6',
        'x1 <= 15',
        'x2 <= 15',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(lb=0, ub=15, vtype=gurobi.GRB.INTEGER, name="algebra_questions")
    x2 = model.addVar(lb=0, ub=15, vtype=gurobi.GRB.INTEGER, name="calculus_questions")

    # Objective function: Maximize 1*x1 + 3*x2
    model.setObjective(1*x1 + 3*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 25, name="total_questions")
    model.addConstr(x1 >= 10, name="min_algebra")
    model.addConstr(x2 >= 6, name="min_calculus")
    model.addConstr(x1 <= 15, name="max_algebra")
    model.addConstr(x2 <= 15, name="max_calculus")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution: Algebra questions = {x1.varValue}, Calculus questions = {x2.varValue}")
        print(f"Maximum Score: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```