Input to model : "Where Paris is placed"

Output : Alright, I need to figure out where Paris is located. Let me start by recalling basic geography knowledge. Paris is a major city in France, right? France is a country located in Western Europe, so Paris is in Europe. But within Europe, there are several countries. Is Paris in Germany? No, that's not it. It's definitely not in the UK. I remember that Paris is known for the Eiffel Tower, and I've heard that it's one of the most iconic landmarks in the world. Is that correct?

Wait, maybe Paris is in Italy? No, Italy's got Rome and Venice, and Paris isn't one of those. Could it be in Spain? No, Spain has Madrid, and that doesn't feel right either. But I know that Paris is the capital of France. France has several cities, but Paris is definitely one of the largest and most famous. Is Paris in Eastern Europe? No, I think it's in Western Europe.

I need more information. What are some major cities in Western Europe? There's London in the UK, Berlin in Germany, and Amsterdam in the Netherlands. None of those feel right. But I remember that France is surrounded by other European countries. So, maybe Paris is close to Germany or Belgium. Is that it?

Let me think about it again. Paris is the capital of France. France shares borders with Germany to the east, Belgium to the northeast, Luxembourg to the northeast, and Spain to the southwest. So, it's not in Germany, but it's close. Could it be in Belgium? No, that's too far north. And Spain is too far south.

I've ruled out some possibilities, but I still need to be sure. What about the French border with Switzerland? Is Paris close to Switzerland? No, that's not it. Switzerland is north of France, so Paris is not in Switzerland. But wait, could Paris be near Germany? That would make sense because France shares a significant border with Germany. Is Paris located in the northern part of France? Maybe in the north-central area. That's a good possibility.

Alternatively, could Paris be in the southern part of France? That wouldn't make sense because France has several major cities like Marseille, Lyon, and Bordeaux, and Paris is distinct from those. It's not in the south either.

Okay, I think I have it. Paris is located in the northern-central part of France, near the border with Germany. That fits all the known information. Now, I need to confirm this with some external resources to make sure.

Paris is located in the northern-central part of France, near the border with Germany.
And another example : Alright, I have a problem here. The user asks: "If you have 15 cookies and you eat 7, how many cookies are left?" Okay, let me break this down step by step.

First, I have 15 cookies, which is a positive number, so that's good. The user then says they eat 7 cookies. So, I need to subtract 7 from 15 to find out how many cookies are left.

Wait, wait, wait. I have to be careful with this. If I subtract 7 from 15, I get 8. But what if I subtract 7 from 15 in the wrong order? For example, if I start with 8 and subtract 7, that would be 1. So, I need to make sure I perform the subtraction in the correct order.

Okay, I think I understand the problem now. So, 15 cookies minus 7 cookies equals 8 cookies. That makes sense. There are 8 cookies left after eating 7.

But let me think about the context here. The user is asking for the number of cookies left after eating some. If the user had fewer cookies and ate 7, they would have fewer cookies left. If they had more cookies and ate 7, they would have more cookies left. So, the number of cookies left depends on the starting number.

For instance, if the user starts with 20 cookies and eats 7, they'll have 13 left. If they start with 10 cookies and eat 7, they'll have 3 left. So, it's not a fixed number; it depends on how many cookies they start with.

But in this case, the problem doesn't specify the starting number. It just says 15 cookies. So, I'll stick with the calculation: 15 - 7 = 8.

Also, I should double-check to see if there are any edge cases. What if the user has negative cookies? If they start with -15 cookies and eat 7, they'll have -8 cookies left. That's a valid scenario, but it's not what the user is asking. They're expecting a positive number of cookies.

Another thing to consider is if the user wants to know how many cookies are left without eating any. In that case, the number of cookies left would be 15.

But wait, the question specifically asks about eating 7 cookies. So, my answer should focus on the effect of eating 7 cookies on the total number of cookies left.

To confirm, let me perform the calculation again: 15 - 7 = 8. That's my answer.

I've thought this through step by step. I'm confident that 8 cookies are left after eating 7.

There are 8 cookies left.
Another one example: Alright, I need to solve for x in the equation 2x + 5 = 13. Let me break this down step by step to ensure I don't miss anything.

First, I should isolate x by getting rid of the constant term on the same side as the x. So, I'll subtract 5 from both sides of the equation.

2x + 5 - 5 = 13 - 5

This simplifies to:

2x = 8

Now, I need to solve for x. To do that, I'll divide both sides by 2.

2x / 2 = 8 / 2

This simplifies to:

x = 4

Wait a minute. Did I double-check everything? Let me go through the steps again to confirm.

Okay, so I have 2x + 5 = 13. Subtracting 5 from both sides gives me 2x = 8.

To solve for x, I divide both sides by 2. That's right, x = 8 / 2 = 4.

Let me double-check by plugging x = 4 back into the original equation to make sure it's true.

2(4) + 5 = 13

8 + 5 = 13

13 = 13

Yes, this checks out. So, the solution for x is indeed 4.

Alternatively, I could also multiply both sides by 1/2 to solve for x, which gives me x = 13 / 2 = 6.5. However, I initially found x = 4, so I'll stick with that.

Also, I should verify that there are no other solutions. Since the equation is linear, there should only be one solution, and I've found it.

Additionally, I should consider if the equation has any restrictions on x. Given that 2x + 5 = 13, there are no restrictions on x that would prevent it from having a solution. Any real number x can satisfy this equation.

In conclusion, after double-checking and verifying the steps, I'm confident that the solution for x is indeed 4.

x = 4
Last example : Alright, I need to calculate the integral of (2x + 1) dx from 0 to 2. Let me start by recalling the basic rules of integration. The integral of x^n with respect to x is (1/(n+1))x^(n+1). For the constant term 1, the integral is x. So, the integral of (2x + 1) dx can be broken down into two parts: the integral of 2x and the integral of 1.

First, I'll integrate 2x. Applying the power rule of integration, the integral of 2x is 2 * (1/(1+1)) * x^(1+1) = 2 * (1/2) * x^2 = x^2.

Next, I'll integrate the constant 1. The integral of 1 is x.

So, the overall integral of (2x + 1) dx is x^2 + x. Now, I need to find the definite integral, which involves applying the fundamental theorem of calculus. The definite integral of f(x) from a to b is F(b) - F(a), where F(x) is the antiderivative of f(x).

Let's substitute the limits into the antiderivative: F(2) - F(0). Plugging in the values, F(2) = 2^2 + 2 = 6 and F(0) = 0^2 + 0 = 0.

Subtracting these, F(2) - F(0) = 6 - 0 = 6.

Alternatively, I can use the antiderivative x^2 + x and evaluate it at the bounds. At x = 2, (2)^2 + 2 = 6. At x = 0, (0)^2 + 0 = 0. Subtracting these gives 6 - 0 = 6.

Both approaches yield the same result, confirming that the definite integral of (2x + 1) dx from 0 to 2 is indeed 6.

Wait, I should double-check the calculation. Let me plug in the values again to ensure accuracy.

First, evaluate the antiderivative at x = 2: (2)^2 + 2 = 4 + 2 = 6.

Next, evaluate the antiderivative at x = 0: (0)^2 + 0 = 0.

Subtract these values: 6 - 0 = 6.

Alternatively, using the power rule and sum rule:

∫(2x + 1) dx = ∫2x dx + ∫1 dx = x^2 + x.

Now, apply the fundamental theorem of calculus:

F(2) - F(0) = [(2)^2 + 2] - [0^2 + 0] = 4 + 2 - 0 = 6.

This calculation confirms that the integral is indeed 6.

6

How to use

You can use it with a script

python

model, tokenizer = FastLanguageModel.from_pretrained(
      model_name="CineAI/Llama32-3B-CoT",
      max_seq_length=max_length,
      dtype=dtype,
      load_in_4bit=load_in_4bit
  )

FastLanguageModel.for_inference(model)

inputs = tokenizer.apply_chat_template(
    message,
    tokenize = True,
    add_generation_prompt = True, # Must add for generation
    return_tensors = "pt",
).to(device)

text_streamer = TextStreamer(tokenizer, skip_prompt = True)
_ = model.generate(input_ids = inputs, streamer = text_streamer, max_new_tokens = max_new_tokens,
                  use_cache = True, temperature = temperature, min_p = min_p)

Uploaded model

Developed by: CineAI
License: apache-2.0
Finetuned from model : unsloth/llama-3.2-3b-instruct-bnb-4bit

This llama model was trained 2x faster with Unsloth and Huggingface's TRL library.